Glad somebody agrees with me about him being Peter Pan! Awesome connections, I never would have thought to analyze the phone.
One thing I noticed on re-watch of Desperate Souls is that Bae says he is 3 days away from his 14th birthday which is when he would be sent off to fight in the Ogre Wars. In Hook, a grown-up Peter has 3 days to prepare to battle Hook.
And then there’s the near constant referral to Bae as being either “lost” or “boy” (Peter is very often called just “boy”).
As Peter Pan traveled back and forth between our world and Neverland it’s entirely possible that Bae somehow ended up there and just got stuck in our world at the time of the curse.
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Keeper of Hook's Trenchcoat.