PBF - Be sure you notify your airline well ahead of time that you will arrive with guns. To my knowledge, UK Export will have to write each gun off of someone's license and that someone must be present. UK doesn't recognize the rook rifle as an antique and requires it be on a license. If you can put it on yours, I think you are OK, but I'd for sure call UK Customs and confirm. You will need to visit Customs and they will want to see the serial before the gun(s) ships. The airline will probably provide you an escort to Customs, and he will walk the gun to the luggage container once the guns clear Export.

The rooker doesn't even have to be declared coming into USA, although, I would do so. If you have presuasive documentation as to the serial date, you should be perfectly OK.