There is no official owner of the frame, and thus no way to transfer ownership or make someone the owner of the frame.
The owner of the frame should simply be understood as the person who owns the frame and physically has access to it. To the frame, every connected phone is simply considered a friend.
However, it is possible to give a friend permission to share the frame's friend code. You can check out this quick guide for more help: How to Share Friend Code From App.
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