Customer return item that's not ours but opened A-to-Z and we lost

A customer returned item that is not ours. We were waiting for Amazon to process the refund so we could open a Safe-T claim but during that time the customer opened a A-to-Z claim. Now Amazon sided with the customer and refunded the customer out of our pocket and we could not upload photo proof on A-to-Z claim that the customer returned wrong item. We lost the A-to-Z appeal because of that. So is that a lose lose situation that nothing could be done?

The order ID is 111-7117736-1893012

@SEAmod