Sold a vintage mug - have my first customer refund request, too

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I've been working on selling on ebay with a friend. We have a store and go "sourcing" about once a week to get "new" items to list for sale. When we first began, mugs were a "thing" and we got quite a few of them. Some have sold very well. Others are slow movers. One of those mugs was for the now-defunct finance company AIM. It FINALLY sold to a finance school grad, naturally. I have it packed and ready to go. Other things we've sold include vintage post cards that were matted and framed, high end ladies shoes and athletic shoes and, recently, a board game produced by Colonial Williamsburg. The board game was in great shape and had all the pieces. The box was torn in two spots at the seams, but I taped it together and pointed that out in the description. It was delivered a couple weeks ago, but just yesterday the person contacted me saying that they weren't home when it was delivered and they just now noticed that it was damaged by the post office - through the box, through the bubble wrap and into the board game itself. Lovely. What was I supposed to do about it. It left my hands in good shape. Plus, it was insured by the post office. They want ME to reimburse them (partially) for the damages since they didn't receive it as offered (OK - and my fault there is???) and want me to file the claim with the PO. I've got to talk to some people because, while good customer service would have me going along with it, I think it's pretty presumptuous for them to even ask since it's obvious I didn't send a damaged item. I'm a little annoyed by it, but at the same time know that if the PO reimburses me fully and I reimburse them partly, I'll still come out ahead. What do you think? I'm still going to ask others in the reselling game what they think, but thought I'd bounce it off you as well.