Hello Alexander Melzer,
Welcome to Microsoft Q&A forum.
Before we proceed, may I have a photo of the issues on your computer and your son's computer to check for you? Please remember to remove all personal information before posting.
Additionally, in your son's computer case. I think that the app is actually asking for the PIN he set for his computer Windows Hello, instead of the account's PIN. You can try to let him sign in with the PIN he used to sign in to his computer.
I'm waiting for your reply.