What happens when a customer online claims they have not received merchandise?

I have sent a book out over TWO months ago. Today I received an email stating they have never received the book and demand credit. I searched the tracking code and the U.S. Post office says it was delivered to them a week later when I sent it.

What happens now? My Track and Confirmation number says it was delivered…but they claim not to have it. It’s also fishy they contact me TWO MONTHS later about not receiving it.

I’m afraid I’ll have to pay them $75….but this is proof that I did send it out right? This is really upsetting.