rehoming process (i need help‼️)

hi! im new to this group, but i have a few questions as ive asked my registered vet and she was almost useless. i posted this in another group but im unsure on if it was allowed in there so im posting it here too just in case🙏
i already have a dedicated new owner for my cat who will be ready to take him in when the time is right (around september-ish). its my boyfriend’s dad who will be taking him in, which is good for me also as ill get to see him again monthly. we live 3 hours apart, but cats are allowed on trains so that shouldnt be an issue. i already plan on using things from my home so he settles and can process the rehoming well, with his toys and some of my blankets so he still has the familiar smell of home.

however, as itll be a private rehoming done myself rather than through a shelter, im unsure of all ill have to do. when i search into it, more or less all that comes up is how the process is when doing it through a shelter or your vets and surrendering your pet. so, id appreciate any help as the vets didnt have any words of advice or how to help me with it.
basically, i need to know how to:
-go about transferring ownership / what i actually need to do with his microchip
-if i need to withdraw him from the vets hes currently at, and if i’ll need to help my boyfriends dad with the process of finding a new vet for him/anyrhing else needed
-basically any advice you can give me.

another issue currently faced is the fact he has fleas and our house is infested even though hes an inside cat. i no longer live there due to my own personal relationship with my family (i live with my nan, about 10 min drive away and an hour on the bus due to the routes) theyve been giving him flea treatment, yet it seems to be fluctuating between working on him and not working. theyve also done house treatments but it may be the products not working right as it isnt doing too much either. i obviously do not want to burden my boyfriends dad with fleas when the handover is done, so does anybody recommend any good products / ways to get rid of fleas most effectively? thank you!!!!