Hi @p6ril yes you may.
I have rings and cards registered on both my phone and tablet, they work fine on either device.
The unlock app registers your UID in the phone. The part that is written to the ring is actually just an action trigger basically, with the UID making that one allowed to trigger the unlock.
You can also use the same ring with an arduino reader that doesn't alter the stored info, just reads the UID, or a door lock that operates off the UID.