It prioritizes the order based on when things dropped, not by rarity. Exactly as it should work.
As for your question about transferring with the app, that's a good question.
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I am well aware how it works, I have been playing since release. It should sort by rarity if your postmaster is full, or at least something warning you that your postmaster is full.
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That's not how it should work. It's just a post master to give you what you receive in the order IT receives things, not a financial advisor there to pick the best things for you to keep.