Android version shows ads despite ad-free upgrade

After getting a new tablet and installing Plants vs. Zombies 1 on it it now again displays ads during gameplay even though it shouldn't since I bought the ad-free upgrade on my old tablet. How can I get the new tablet to know that?
Also is there any way to get your progress from the old tablet to the new one? Both are Android, both from Samsung (Galaxy Tab A6 and A8), and while it wouldn't be too bad to play through the game again, it would be nice if the ad-free upgrade at least worked.