I have followed this topic closely and quite a lot of experience of it. My own experience is two types:
1. Where the original purchaser of Apple is known and requests the transfer. This is your situation and should not be a problem.
2. Where the original purchaser of Applecare is not known. This has happened to me buying used items from the national exchange chain CEX in UK. When I get the new device home and fired up, Settings > General > AppleCare & Warranty sometimes shows the device has AppleCare until some date in the future. The first time this happened I phoned ApplCare and explained situation. The reply was that there is no way it can be switched without the request of the policy purchaser and I can not take out a new plan, BUT the device remains covered unless the original purchaser cancels it and claims the refund. Applecare stays with the device...so even if you don't transfer AppleCare to your son it will still be covered. You can check in Settings > AppleCare & Warranty.
I am not very happy only having Applecare as long the unknown previous owner doesn't cancel but there is nothing I can do about it. The AppleCare guy's attitude was "you got lucky" and I did in a way. I have never had a previous owner cancel and suspect many people don't realize how easy it is to do and get a refund....I always do this if applicable.
I have just experienced one complete exception to case 2 above, which seems a complete mystery. I recently purchased a 2+ year old M1 MBA. I was not at all surprised that Settings > AppleCare & Warranty said all cover had expired. However I was very surprised when a few weeks before its 3rd anniversary, I saw in Settings a notification that Applecare was about to expire and did I want to extend it for a year....which I did with a new policy in my name. Why did it say all cover expired?