The buyer was the victim? Why?

The timeframe worries me. They waited until the last moment to request a refund for something they've probably had and been using for 5 weeks.

Tell them to open a case with Paypal. Or has the Paypal time limit of 45 days already expired? I'd be telling them to whistle.This will require them to return the item, by trackable means, at their expense. That tends to sort out the pretenders. Unless you have already initiated the refund. If not, don't. You can add funds to your Paypal account from your bank account (which takes 3-5 days anyway), but I would be highly suss about this one. 

Unless you have very good evidence that the item is in fact defective, why are you offering to refund? Please don't roll over unless they have a compelling case for a refund without return. They will then try it on with other sellers.

it is also a good idea to keep enough in your Paypal account to cover a couple of refunds. I've never had to do so, but I always can.