Buyer reached out about defective product

Except she’s part of the Vine program. I gave her my copy paste customer service response, but that’s reserved for customers. Should I still reship her item..? Feels a little strange giving out 2 free items to someone.. lol

“Hi there ! Firstly, I’d like to apologize about this. It’s certainly not to supposed to happen, and I’m working to resolve things so it doesn’t happen again. For the resolution, I’d like to replace your item for free right now. Can you confirm your address so I can remake the order and send it out?”

Is the email I sent in response (on amazon)