Why would someone who is a permanent resident need an I-797?

Question

I was recently helping my long-term boyfriend file some papers and I saw this form. I remember that my friend Claire had one since she applied for what I think was an H-1 visa.

Answer 1

That is for non nationals ie. federal citizens

Answer 2

An I-797 is an approval notice that is sent out by USCIS for approved petitions. Your boyfriend would have received an I-797 at some point during his application process to become a permanent resident.