I am the SPED teacher. Would be nice if rewards were in my operating budget. I think (assuming he makes it to the end of the week) he does deserve it, because for him that's a major achievement. He's a good, well-meaning kid with real difficulties controlling himself. I want him to both behave for a while and accumulate reasons to believe in himself.
I have given multiple basketballs away in my 30+ years of teaching PE. My dad has gotten me many from garage sales and some just show up on my playground. If I have a kid with a real interest and no ball I sometimes give them one I dont use. I never use full sized ball in PE so I give those away.