Sounds to me like Hanlon’s Razor may apply here.
Ordinarily this has all the hallmarks of a scam; however, you have the phone and it works. The only thing I can possibly think of is that once you’ve paid by bank transfer she’ll reverse the PP refund she’s given you (if that’s even possible) so that you’ve paid twice. You’ve paid by PPG so that’s lost money, she’s ‘refunded’ by making a normal payment, you bank transfer, she reverses her PP transfer, boom.
When you picked it up from her employers, are you certain it was her employer and not a car park where she went “I work here, honest”?