Thank you Andre for you quick response!
Yes I am using the same Google account, and I can find the Poweramp Full Version Unlocker in Play Store. However, it has a price tag attached. When I try to install I end up with the message box which has only one choice to continue: "Kaufen" (= purchase). I have uninstalled Poweramp app plus Unlocker from my old tablet but this doesn't change anything.
Interestingly, it does seem to make a difference from which device I access Play Store (using the same Google account). On my old tablet I see the Unlocker without price tag, on the new tablet as well as on my PC it has a price tag.
For other apps that I purchased (eg Sun Surveyor) I didn't had a problem to install it on my new tablet.
Is there a way to transfer the unlocker between the tablets directly?