treppenwitz

No.
 
https://egov.uscis.gov/e-request/displayTypoForm.do?entryPoint=init&sroPageType=typoError submit correction here.

AP Approval Notice

EAD Approval Notice

The card comes in a Priority Mail envelope; see below:

i-797s are needed for someone that has an immigrant petition (I-130). 
 
In the instructions it notes that k-1 visas are different due to them being a non-immigrant visa and all that is required is a copy of the visa and the I-94, and a marriage license. But there is no underlying petition because the I-129f petition is one, not an immigrant petition and two, already approved and completed as its purpose was to allow your foreign fiancé to apply for a fiancé visa.
 
 
Instructions for form I-485:
“Unless applying under INA section 245(i), most Form I-485 applicants must submit photocopies of documentation showing they were inspected by an immigration officer and either admitted or paroled into the United States. The following types of applicants do NOT need to submit documentation of inspection and admission or parole: registry applicants, asylees, VAWA self-petitioners, special immigrant juveniles, T nonimmigrants applying under INA section 245(l), U nonimmigrants applying under INA section 245(m), and individuals born under diplomatic status in the United States.

You must establish any claim that you were admitted or paroled into the United States.
This evidence must relate to your most recent arrival into the United States. Submit copies of the following documents, if available:
A. Passport page with admission or parole stamp (issued by a U.S. immigration officer);
B. Passport page with nonimmigrant visa; and
    Form I-485 Instructions 12/13/17 N Page 9 of 42
  C. Form I-94 Arrival-Departure Record (See Form I-94 Arrival-Departure Record in the General Instructions section of these Instructions).”
 
 
“Filing Your Form I-485 Based on a Category That Does Not Require an Underlying Petition

If you are filing your Form I-485 based on a category that does not require an underlying immigrant petition, you must submit other documentation. See the Additional Instructions for more category-specific information.
 
Additional instructions
 

Nonimmigrant fiancé(e) beneficiaries of Form I-129F always have a visa available, but may file Form I-485 only after marrying the U.S. citizen (Form I-129F petitioner) within the requisite 90-day period after admission to the United States on a K-1 visa.

In addition to the evidence listed in the What Evidence Must You Submit with Form I-485 section, you must submit

a copy of the marriage certificate to show that the K-1 nonimmigrant fiancé(e) married the U.S. citizen (Form I-129F petitioner) in the 90-day period. This additional requirement applies to both K-1 principal and K-2 derivative applicants.”

Why are you looking to get another copy? 

You shouldn't need a copy of the I-797 for the I-129F unless you want it for your own records. When she goes to AOS she can provide a copy of her visa in her passport with the I-94.

File I-90 and then book an info pass to get the stamp in his passport. 

Before you send in the wrong card get the USCIS verbiage removed from your ss card. Update your drivers license as well. 
Use only ss card and dl for employment purposes. 
The correct GC will take at least 6 months. You can file online but you have to send in the wrong card as well or they’ll reject your filing (so make plenty of front and back copies - or scan). 

Most of them marry beforehand (anywhere in the world) and then file a spousal visa. A K-1 visa is a very odd choice for a couple living together overseas. It’s more suited for couples who cannot get married overseas because the USC cannot get time off work, cannot get a visa to travel to the location, or the marriage process in that country is complicated or impossible for foreigners and where the foreigner cannot get a B-2 visa to visit the US and marry here. Others chose it because they don’t want to be apart after marriage. That’s not a concern for you. 
 
As it stands, you are doing an overpriced tourist visa that will give your fiancé little more than tourist status until you get married AND pay even more money and wait many months for your fiancé to even be able to get a job. Green card comes even more months later. Why would you do that if you have an alternative? In some states K-1 folks can’t even drive until they have an EAD. If you marry and apply for a spousal visa she will have a green card the minute she lands at the airport and all the privileges that come with it. 

Someone correct me if I’m wrong, but if they are already in the US then OP should be able to file now for them as stepchildren under the IR category (without them having to leave). That’s not the same as intending to bring them in at a future date with the intention to change status. 

It expired while outside the US?? Okay then, that's a very, very different issue. Presumably his AOS application will be deemed abandoned. To avoid a pending AOS application from being abandoned, one must leave and re-enter the the US with valid AP (exceptions apply for certain work visas).
 
There are some people who lost or damaged AP while abroad, and the embassy/consulate was able to assist them.
However, his case is very different in that he has no valid AP right now and is outside the US. Presumably he will need to start over with the CR-1/IR-1 spousal visa process.

@GYnot, if your I-485 receipt notice starts with MSC then send the I-131 to the Chicago Lockbox: https://www.uscis.gov/i-131-addresses

Okay, thank you. And I assume I'm fine with saying No on item 14. That asks if I want the SSA to issue me one, since I have already done so. 

Answer "No" since the SSA still hasn't issued the number.

Renewed? No. Can you you get a new one? Sure.
 
File the I-131 and wait. Attach a copy of the I-485's receipt notice (NOA1) instead of payment (no fee when filed in this case).

They are not deportable due to their presence in the US while covered by any period of authorized stay. They can be deportable for other reasons, as applicable, but not due to just being in the US.
Correct on the part about not accruing unlawful presence.
 
Not quite. Previous unlawful presence is not erased or forgotten just because AOS is approved. This occurrence only impacts people in specific circumstances, but it does exist.
For example, say somebody came on the VWP and overstayed. They then married a USC, filed for AOS, and got a green card. If they later lose/abandon their permanent residency (voluntarily or otherwise), they are still prohibited ever using the VWP again due to their past overstay. No 3/10 year bar is applied, but there are still immigration consequences.
 
Correspondingly, a denied AOS application does not retroactively apply unlawful presence. This isn't strictly always the case (i.e. if you file an application that grants an authorized stay that is deemed frivolous), but it is the general case.
 
He has no current legal status (which is not the same as having any sort of unlawful status).
He has a period of authorized stay granted by the AG.
He is not accruing unlawful presence.
 
Edit: Also...
He is eligible for work authorization (EAD).
He is eligible to request permission to re-enter the country (AP).
These 2 items are eligible benefits, which are yet again different than any sort of legal status/authorized stay/unlawful presence.

Good points raised about being out of status and not able to travel and such. But I would also add that by delaying to file for AOS, if something did happen and the relationship fell apart, she would have been up the creek with no paddle, and facing a 10 year ban upon exit from the US. If she had a child with her spouse as well, she could be separated from her child by leaving (including if she got deported). It’s really a bad situation to be in all around. While ROC is a PITA, the benefits of waiting to file AOS versus the risks just doesn’t sound like a wise decision.

If he reaches the POE prior to turning 21 then he's ok. Otherwise your looking at a long process.

The online system is known to have these types of glitches. Good news is that its a non-issue.

Most binders are not an issue. USCIS just has the following preference; https://www.uscis.gov/forms-filing-tips
 

He will age out before the visa will be issued.  He will not be eligible for a K2

Very true. Both the I-129F and I-130 instructions state that the following stuff should NOT be included:
https://www.uscis.gov/i-129f
https://www.uscis.gov/i-130

DACA is not completely free, but still too cheap IMO.
Biometrics: $85.00
I-821D: $0.00
I-765: $410.00
Total: $495.00 for employment authorization during the 2 year period of deferred action

Somebody is extremely unlikely to actually be deported in 2 months.
 
While still pretty unlikely, getting a Notice To Appear (NTA) in that time is much more likely than actually being deported. Once an NTA is issued, you can no longer file for AOS with USCIS - you would need to have an immigration judge address your case first. That process would entail a lot of unnecessary time, stress, and additional costs.
 
In that time with even just 15 hours of work per week, 50 weeks annually, at the federal minimum wage you could have earned a few times the amount needed to pay back the filing fees.
 
It is what it is now....no way to go back in time.

These instructions are still current:
https://www.visajourney.com/content/ssn/
 
Essentially, fill out an application form, print it off, and bring it with you along with your passport and printed I-94. Walk in to your local social security office with these documents and tell them you are applying for a social security card for the first time. They will take copies of all of your documents, and create a case in the SAVE system to verify your immigration status. Once confirmed, you will be issued with a social security card. The process was all very straightforward, at least at my local office.
 
You are actually able to track the status of your SAVE case using this system by searching for your passport number. Once the case shows as 'returned to agency' then your status has been confirmed, and your card will be mailed to you by the SSA. The whole process took exactly 2 weeks, from visiting the office to receiving my card.

I would immediately speak with my HR dept and insurance carrier and ask them to add her immediately while you wait for a SSN.  

1) Limit unsupervised contact. You don't want him to even try to claim abuse. Somebody who deceives and lies like described is probably willing to do anything to get what they want.
2) Contact USCIS to withdraw your I-864. No I-864 = AOS cannot be approved. This will need to be in written form, or you can schedule an InfoPass appointment to do so in person.
3) No show at the interview = they won't approve AOS. You could appear, withdraw the I-864, and explain the situation there but it seems like an intense situation may develop.
4) Material misrepresentation on an immigration form is a permanent bar. If you have evidence of any of the false information submitted, you can submit that as well. It won't hurt to submit evidence of the divorce as well.
5) Bigamy is a crime.