Have you gone to SS and talked to them. Your Mom is not the only person who has been in this situation. I don't think a lawyer is needed. Did u talk to the SW at the facility. This should not be something new to her.
For legal authority for her other affairs (like medical and other financial) you will probably need to seek guardianship, but you will need to find out what's possible in her county/state. Consulting an elder law attorney for this will give you answers.
When we did this for my wheelchair bound MIL in MN they made us bring her in with a hard copy of the death certificate, so I'm hoping they can just call cause it was an ordeal to get her to the SS office.
Have you gone to SS and talked to them. Your Mom is not the only person who has been in this situation. I don't think a lawyer is needed. Did u talk to the SW at the facility. This should not be something new to her.