Old-timer registration and registration number

Moin, when I went through the old vehicle letters from my Audi, I noticed that the previous owner, who had already driven the car with H-approval, only had county + letters + numbers as official registration number. So without the H. To my knowledge, this is actually correct, because the H does not belong to the official registration number, but is only an addition. However, with me the H is also registered as official registration number. What is correct and would it theoretically be possible, a second vehicle with my registration plate without H, since it would not be the same registration plate on the paper? And how is that with you in the registration plate? Does your official registration plate with the numbers stop or is the H with you?