jagaimo

Send them a copy of your brother’s birth certificate and your birth certificate which should have the same name for parents. 

When you get back, file a request for a replacement green card and have it sent to you new address.

The elephant in the room is that to solve the problem, the applicant must admit to having committed a material misrepresentation in the prior visa application process.  Once he does THAT, they have sufficient grounds to find him ineligible for the visa, or at USCIS simply deny the petition.  If it's USCIS, there can be an appeal.  If the Consulate, a waiver can be tried.
 
This is what happens when people lie on immigration forms and/or to immigration officials.  The only results I've seen in these situations have been petitioners giving up on the relationship and divorcing.  I'm sure there are other results, but we don't hear about them here.  My "results" cited were not read here on VJ.

Your son needs to return before his authorized stay is expires. There is no point in a lawyer as he is not eligible to AOS

Here is exactly what you need to do.  There is no quicker way through you.
 
1. You file an I-130.
2.  You will get a receipt with a Priority Date.
3.  Follow the Visa Bulletin to see when your son's PD will become current.  The current wait is 6-7 years.
4.  At some point during the wait, USCIS will approve the I-130 and send it to the NVC where your son will need to wait for his PD to become current.
5.  When your son's PD is about to become current, the NVC will process his case further.  You send in more paperwork and then your son interviews for an immigration visa in his home country.
 
While waiting, your son can continue to use his visitor visa to visit.  
He must remain unmarried to stay in the F1 category.  If he gets marry, his wait will be 12-14 years.
 
What country was he born in?

You have one valid passport.  Complete the DS260 present tense questions in the present tense.