Your options are clear:
You can accept the return or send a full refund without getting the item back.
Messaging the buyer will only delay things - if you don't accept the return or refund in full, they will be able to ask Ebay to step in and get a refund without sending the item back.
Accept the return and supply a label.
Then refund once you get the item back.
You can report the buyer if you want to for opening a return for a false reason but I would just advise you to accept the return. As you can see, refusing a return is not an option unless the buyer received the guitar more than 30 days ago.
"There are two ways to be fooled. One is to believe what isn't true; the other is to refuse to believe what is true.”
Søren Kierkegaard, Danish philosopher (1813 - 1855)