First, never replace an order until you receive the first shipment back or the post office notifies you that the package has been lost. If the customer has it delivered to a PO box it is their responsibility to pick it up. Did you explain to the customer that she must go to the post office to pick up her package? She may be under the misimpression that she placed an order that was to be delivered to her home address.
Second, do not enter into conversations with a customer about orders that were not purchased from your shop. Simply inform them that those orders were not purchased from you and if you have a kind heart and a little time, explain how they can look at their previous orders to find the correct seller.
I had a customer contact me on Amazon one time and she had never ordered from me on Amazon. She had ordered from me previously on Etsy. When there is any question about an order, I always search the orders on both Amazon and Etsy by customer name and order number. So third, look up any orders placed by that customer by name. And if you sell anywhere else, check the orders there too.
Deal with customers only through Etsy! If this person that you emailed says she is not her contacting you, then could it be someone else in her household using her email and Etsy account to place orders? I know my grandkids used to use their mom and dad's accounts to place orders on Amazon until they were grown. So if there are others in her household, she needs to check with them.
Finally, be very careful that this is not a very complex scam that has been orchestrated. Just tell her that with all of the issues you cannot ship or refund anything until you receive your previous shipments back.
UPDATE: Just saw your post that was done while I was typing. If it is not at her post office, file a missing or lost shipment with USPS. You can do that online.
