Mover minor's account to new computer but keep old computer account active

My son has a child/minor account on my iMac. It's a family account. He has his own username and password and iCloud access. We recently bough him his own MacBook. I can not figure out how to connect/configure this new MacBook to his iCloud account. During setup the MacBook will not let me log into his account, keeps saying password is wrong, then it freezes it.... but then I go to the iMac and I'm able to login into his account with his password that the MacBook thinks is wrong. So I gave up on that and logged into the new MacBook with my account and it worked. Now I'm trying to add my sons child/iCloud account as a user to this MacBook and it can not be anymore difficult. I have no clue. He shows up under family, but when I logout it only has me as a user to log back in. I go to Users & Groups and add account, but this wants to create a whole new account, I Just want to use his existing account. Also I want to keep his account on my iMac, so he can either login to my iMac (as he has been doing) under his own account to login to the new MacBook under his account. Any ideas on how to make this work?