"He lives with his mother."
Translation:Han bor hos sin mamma.
I guess you know that better than I do :). "Hos sin mamma" means that he lives at his mother's place, and, at least to me, that she is living there as well. If his mother owns the house but doesn't live there herself, I would probably say "han bor i sin mammas hus" or "han lånar sin mammas hus".