as I known, if you have H1B, you can come back before ending your H1B.

I would advise you schedule a consultation with another lawyer. Also it doesn’t hurt to try emergency parole. Being that he is gravely sick, you just may get it

do you know what center is processing your AP? I would suggest booking an in person info pass appointment through the website, don’t bother with the lawyer as it won’t cost you, take any evidence you have to support an emergency expedited AP. they approve on a case by case basis so there’s no harm in trying! if you want to chat to a real person for specific steps just chat to the Emma bot on the uscis website and ask to be transferred to a human :) good luck!!

I got an emergency AP from my field office in May. same case as you. I called uscis and told them the situation. The next day, a USCIS officer called me back and after I explained asked if I had the death certificate. I said no but that I could get it so they scheduled an in person appointment for me at the nearest field office. I went there next day with a scanned copy of the death certificate and proof of relationship, they gave me the emergency AP right there at no cost. It took about 3 days from the day that I called. They had initially said the closest appointment date was 3 weeks so I said to them that it was of no use then cos I would have missed the funeral which was one week from the day I spoke to them. i went ahead to tell them never mind I would just keep waiting for GC. But then they called me back the next day with appointment date for that morning and asked if I could make it, I was like sure thing!