echo924

No.  Your husband will not lose his status as a legal resident.  USCIS offices can place I-551 stamps in his passport if his extension letter is near expiration.  That stamp is merely evidence of his status....it is NOT the status, itself.  Only an immigration judge can remove a person's LPR status.....
 
EDIT:  We filed my wife's I-751 in March 2019.....still waiting, too.   I'm not worried about her status......and you shouldn't worry either...🙂

USCIS will still address emergency situations........but with or without the stamp, a person still has LPR status until an immigration judge rules otherwise.  The stamp is only evidence of status.  

You can send it the following day. And you don't have to overnight it either. Priority Mail via USPS is totally fine. It'll get there in 2 days. I would suggest overnight it if the green card expires in 2 to 3 days but if you have ample time to mail it, there is no need to express mail it. Also, you don't have to send it exactly on the 90th day mark. As long as it is within 90 days before the green card expires you are good to go in submitting the packet. I will give you an example. With my greencard expiring on August 28, 2019, my 90 days actually begins on May 28, 2019. I have from that date til before my green card expires to send my application. I could have submitted that early but I didn't because I waited til I have all bank statements and bills from May to include in the packet. I sent mine on June 11 and they received it last June 13. Just don't submit it earlier than the 90 day mark because your packet will be sent back to you. All the best!

He can still submit it with a copy of his NOA1 from his AOS 

Yes, you can file for AP still. Attach a copy of the NOA1 from AOS to the packet to avoid having to pay the I-131 filing fee.

I think you can submit AP any time.  The instructions for the I-131 form state the following:
 
"NOTE: If you filed Form I-485 on or after July 30, 2007, and you paid the Form I-485 application fee required,
then no fee is required to file a request for an Advance Parole Document or Refugee Travel Document on Form
I-131 if your Form I-485 is still pending, if:
 
1. You now hold U.S. refugee or asylee status, and are applying for a Refugee Travel Document (see Part 2. Application
Type, Item Number 1.b. of Form I-131); or
 
2. You are applying for an Advance Parole Document to allow you to return to the United States after temporary foreign
travel (see Part 2. Application Type, Item Number 1.b. of Form I-131).

Under these circumstances, you may file Form I-131 together with your Form I-485, or you may submit Form I-131
at a later date. If you file Form I-131 separately, you must also submit a copy of your Form I-797, Notice of Action,
receipt as evidence that you filed and paid the fee for Form I-485 required on or after July 30, 2007."

If you read through this thread you'll find that lots of us travelled in that situation, and hardly anyone had any issues. He'll probably find he isn't even asked who he is visiting. Best course is to give accurate honest answers, but no more than necessary
- What is the purpose of your visit?
Vacation
- Where are you staying?
(give name of city/state)
- What are you planning on doing here?
Visting XYZ theme park, going to see ABC monument, etc
But if they ask who you are staying with, be honest. Fiance, not "a friend". If you're honest about it, and don't attempt to hide it you're much more likely to have no issues, but at the end of the day its better to be denied entry for being honest, than be denied entry for lying (that would affect future immigration plans)
Evidence that K1 is applied for, well progressed, and likely to be approved are very convincing too, so bring those along - it shows that you're doing things properly.

To minimize the time it takes to work--
1) Get your AOS paper work as filled out as possible before he arrives. Learn it while he's doing the London part.
2) Marry the week he arrives. Find out all about marriage licenses and judge weddings before he arrives.
3) Find out how quickly you can get the marriage recorded and the certificate issued. I got mine next day.
4) Mail the AOS with work authorization application as soon as you get the marriage certificate issued.
Work could be approved in 60-90 days. Greencard can take longer.
Have a fancy wedding ceremony and reception whenever if you want one. People don't even have to know you actually got legally married prior to your big shebang.

Just an update :-)
May 16: Mailed Packet
May 26: Received email/text notification
May 31: Received paper confirmation
Also wanted to say that Visajourney.com has been a lifesaver and made the process SO much more clear. Now we for the waiting game!