However, it is completely your decision if you want to provide a refund.
Also, upon reviewing the order id, I request you to remain assured that the buyer has not filed an A-Z guarantee claim nor did he leave any negative feedback on the product.
Even if the buyer leaves a negative feedback or files an A-Z Guarantee claim, since there are already enough proofs of your correspondence with the buyer, you do not have to worry and Amazon will definitely give you an option of submitting proofs in your defense.