Not sure when DH will actually be starting at the new job, but if possible, could he organize his templates, instructions, etc. from his old job and pass them on to a co-worker? That way if someone calls about one of those items, he can say, "Actually I gave them to Bob before I left, he'll be able to find it faster than I can," or "I think I left that with you guys, check the blue binder." That way he's being helpful, but not actually spending a lot of time on helping people.
I do think he ought to act professionally, especially since he's still with the same company; but regardless of whether he left under happy circumstances or not, there's a limit to how much his former co-workers should be asking of him. His first loyalty should be to his new job. Quickly directing them to Bob about a template, or answering one question, would be okay; but if it's something that's going to take more than, say, 30min to do, it's getting into weird territory. If he does get a lot of calls like this, I think he should talk to his new supervisor about it and ask what level of support he's expected to give his former co-workers. That would be my advice for anyone who's transferring between two branches of the same company, no matter how he left the old one.