I’m sure only working 4 hours a week shouldn’t be a problem. With ssdi you can make like $1600 per month I think. They probably want to see paycheck stubs or something.
How long has he been working four hours a week? If he tells them he has been doing it for awhile but he just got around to reporting it now that could be a problem
I don’t know the income limit when you’re married. I’m on SSDI and have worked my entire adult life part time. My income cap on top of ssdi is $1400 before taxes. Working part time hasn’t disqualified me at all, and I generally work 15 hrs a week.