i've never gone thru USPS for this, so I can't directly answer you, however at the previous job I was at we shipped computer equipment all the time thru UPS and when something was damaged or broken, they were real dicks about getting compensation, even when you paid up on insurance.
More often than not, they would deny the claim based on it's packaging, so it's super important that you (hopefully) read up on packaging/shipping and followed their guidelines
My advice to you is to read up every word they have documented on their insurance claim policies and packaging/shipping and make sure that you were in complete compliance of them. You will need as much proof as you can, so any photos that are dated will be best, and i'm hoping you took pics immediately prior to shipping, and that the FFL has pics. Further, did the FFL open the package in front of the person delivering it? That would further help the case, as a USPS employee would have seen the damage as it was opened.