i agree with givelove.
let us consider how he ended up living back at his mother's house. he made numerous choices over time which led to this situation. it is best to not meddle and let them suffer the consequnces of their choices. it appears this really is the best way for them to learn how to make better choices for themselves.
from what you've explained, it sounds as if perhaps he would prefer to live with you and have you to provide
1. his roof
2. probably his food
3. his emotional support system
4. probably the housekeeping, bill paying, meal cooking, laundry washing, etc.
he is a grown man. he would do well to learn to provide those things for himself.
and once he has settled into your nest, it will be much more difficult to keep your distance from him and his recovery.
he is safe and sound at his mother's. he might not like it, but then again, he can always take some action to get on his own two feet. or not.
and, if you take him in, what if he relapses? then, you're back in the firing lane.
just some food for thought.
naive