I sold an iPhone 4S on eBay, shipped it with signature?

The buyer contacted me through a message on eBay and asked when I would be shipping the phone, and I wrote her back. When I went to print the shipping label through PayPal, it said it was not a proper address because it was a PO Box. It had to have signature confirmation, and I wrote and told her that. She wrote me back and gave me another address. I printed the label and had it picked up by my post office and sent priority mail. I kept checking tracking, and it showed out for delivery on July 3rd. Then that is all. It never showed the status as delivered. I called the post office there, and they had no confirmation and no package and were rude to me. I just figured she got it, or I would hear from her.
Then just today, I got a message from PayPal that the buyer had filed a dispute, claiming she had not authorized the transaction. She never contacted me at all. Then I contacted her and told her if she did not authorize it and wanted a refund, I'd be glad to, if she sent the phone back. She wrote back and said that she does not even have an iPhone and didn't authorize it. The message said "Sent from my iPhone". I contacted PayPal, and they said I'm covered by the seller protection, but they have to investigate. They said if I can get a tracking showing it was delivered, they would release the funds to me.

I hope you got insurance on the package… It sounds like the post office *** up and lost it (or someone stole it)…

It would say delivered if it was…

SO SHOW THEM THE TRACKING NUMBER YOU HAVE THAT SAYS ITS OUT FOR DELIVEY! Out for delivery means it has been delivered and if you got the ebay messages from her iphone then that proves to ebay she's a liar.