Customer claims package not received [Amazon Canada]

I’m a FBM seller and recently got a refund request from a customer, whose message was “Package did not arrive was given a message unable to deliver ” but the tracking information shows that the package was delivered and the recipient signed for it, one hour before he made the refund request.

The package was sent via Canada Post as Amazon.ca does not provide the “buy shipping” option for Canadian sellers. I replied to the customer asking him to reconfirm if he has received his package, who signed his package and if he would give a phone number he could be reached at as Canada Post would need it in order to investigate his claim, but no response whatsoever. What should I do?

As a side note, this isn’t the first time that a customer messaged me regarding an issue with their order but when I try to communicate with them with offers of solutions, they don’t even respond. What am I supposed to do in such situations?