Unless the original packaging material was preserved as the package was opened, and is available to the shipping company for inspection, they will not normally accept a claim for damage in shipping.
And if the shipping carton and materials don't show any damage, I'm confident no claim for damage in shipping would be supported.
If the buyer didn't preserve the shipping material, I would expect that no claim would be honored.
And my experience has been that any claim must be filed by the person who shipped the package, not by the recipient. The shipping company has no contractual relationship with the buyer, only with the person who paid for the shipping.