It actually wouldn't be SSI.

He maybe had enough work credits, he maybe didn't. Call your local SS office to set up an appointment.

You would file for survivor benefits for your grandson. If his mother received custody, she would receive the monthly benefit. There are restrictions on what the money can be spent on and SS makes you fill out a form accounting for the money spent.

If your grandson has a disability himself, he might be able to qualify for SSI, but this doesn't seem to be what you're asking about.