There’s no such thing as “ownership” on Android for apps, any app with enough permission can install updates. The main thing is that F-Droid builds apps from source and signs it with its own key (unless the developer opts-in for reproducible builds). So, the only thing you have to take care of is to make sure to install the F-Droid version from adb.
Maybe this helps: How to backup F-Droid apps in case I lose my phone - #3 by TheLastProject