Yes you will have to refund, what good is any of it to you?

A buyer opened a case against me, saying that the vintage tv lamp was broken on arrival and asked for full refund. He sent a picture that only showed a couple of pieces of the lamp. I agreed to refund after he returned the item. The box I sent him weighed 11 lbs 9.4 oz. The box I got back weighed 3 lbs, 4 oz. More than half of the lamp is missing, including the 3 pieces visible in the photo that he sent. The piece with the signature mark on the back is missing. Even though I agreed to a refund, do I have to refund for an incomplete return? Please help soon before my 3 days are up.