I worked under a manager X in my previous company. Then he moved on. After that I got interview in his company and I cleared the process. First I was unsure wether to join the company or not as I had to relocate to a totally new place. Luckily, I was supposed to join the team lead by X. So i joined. Now after 3 months he moved to a different team but I want to work with him as it was my primary motivation to join. Shall I tell HR and management that I want to work with him. Although I have no issues with current manager or team as well.
Shall I tell HR and management that I want to work with him
If you have no problems with your current manager, then no.
I would refrain from doing this as it makes you look like you want to move for the sake of a single person. Unless you have issues in your current team then there should be no reason to move. All managers will be trained and hired specifically to do this job (Although some don't do it correctly).