Setting up 2 xboxes for my son. One at mine, one at his mother's house.

I find it surprising but I can't find an answer to my situation on here. I hope you all can help.

I separated from my son's mother a while back. I'm looking to get a place of my own soon and to have my son to stay. I have an box Series X, he has an Xbox Series X at his mother's house. I'd like to get him an Xbox Series X for my house too so we can play together in different rooms. Before I do that, I'd like to know how I go about setting this up. I realise there is a "Home" console for every account. The problem is that his home account is at his mother's house and I want to be able to set him up at mine as well so he doesn't have to lug all the equipment to and from her house. How do I go about setting this up? I'd rather not have to buy a second account for him just to do this as he'll lose all his games when he stays with me.

:)