Is your Mum happy to have him living there with her, she may like the company and a bit of help with practical things around the house, or she may just not have the courage to ask him to move out..
We had a similar situation with my brother, he asked to move in with my dad for a few months temporarily when his marriage broke up, he never moved out. My dad was living quite happily on his own, he would regularly ask me if my brother was ever going to move out, in hindsight I think my dad wanted me to intervene, but I didn't and I regret not doing it.
My brother paid for nothing. I had bought the house for my dad so he had no mortgage, he was on a tiny pension, so I covered everything to do with the house, council tax, insurance, repairs, upgrades, etc. My brother lived there for almost 20 years until my dad died and never paid for anything or helped out around the house. . He did help out somewhat with my dad's care in his final years, but he really resented it and tried to convince us to put dad in a care home which he did not want. Said he couldn't cope with my dads illness, so we said, okay just move out as we intend to keep dad at home, as per his wishes.. But of course he never did move out. We hired full time carers for my dad at huge cost, even when my dad was bed bound, we had private carers come in so my brother didn't have to deal. He would be upstairs in his room on the weekend, and we had expensive carers sitting in the room with my dad because my brother didn't want to deal.
When my dad died, my brother expected to remain in the house, I offered to sell it to him at a cut price but he 'didn't want to buy it' just live there, i.e. I would continue to cover all costs associated with the house, he never even suggested paying a rent, he just wanted the status quo he had of no living expenses like when he lived off my dad. . I did sell the house and shared the proceeds of it equally with him and my other siblings, the same as if it was an inheritance from my dad's house.
My brother has never spoken to me or my other siblings since (who had nothing to do with the selling of the house) He and his daughter have badmouthed me to every relative under the sun, that I 'kicked him out' after 'all he did for our dad for 20 years'. Which is absolutely laughable, No one knows he lived off my poor dad for 20 years, he never even took my dad out for lunch once during the 20 years (17 of which my dad was in perfect health). My brother has a very well paid job, probably earning 10x my dad's small pension, and yet he still expected to live off my dad.
Sorry for the stream, your post just reawakened all those memories for me from 2 years ago.