First of all I just wanna say that I really appreciate how much you care about him and want to accommodate him. As someone who stutters that’s so awesome to hear. Why can’t more people be like you!! Yeah I would say not completing his sentences is a big thing. Something that drives me insane is when people smirk, cringe, or awkwardly look at the floor when I try to speak. It’s infuriating. Just look him in the eye (as you would with anyone, don’t stare), give him a reassuring nod and smile, and let him finish his thought. Maybe you could also bring it up with him directly and see what he thinks. I think that would be the best way to find out how to support him. And it would be a good chance to express your thoughts to him and voice your support and tell him he can speak however he wants around you.