Here’s what you’ll need
https://support.apple.com/en-us/HT202712
OP, if the previous owner (who is the original owner) sold you the phone and then transferred AppleCare to your account as outlined in the link cited, you should be able to get this problem cleared up. As others stated, the original owner should be able to go to the store where the phone was purchased and get a receipt printed, to give to you. To make it easier, have him go with you to the Apple Store with original receipt in hand. If he is unwilling to help you, you will end up with a paperweight. Unless he has not been honest with you, it shouldn't be a problem for him to get the receipt and help you out. It is rather strange that you have spent so much time on this, when the remedy is at hand.
- The AppleCare agreement number from the Proof of Coverage certificate
- The serial number of the device your AppleCare plan currently covers
- The new device’s serial number
- Your original sales receipt for your AppleCare plan and both devices
https://support.apple.com/en-us/HT202712
OP, if the previous owner (who is the original owner) sold you the phone and then transferred AppleCare to your account as outlined in the link cited, you should be able to get this problem cleared up. As others stated, the original owner should be able to go to the store where the phone was purchased and get a receipt printed, to give to you. To make it easier, have him go with you to the Apple Store with original receipt in hand. If he is unwilling to help you, you will end up with a paperweight. Unless he has not been honest with you, it shouldn't be a problem for him to get the receipt and help you out. It is rather strange that you have spent so much time on this, when the remedy is at hand.