You'll have to get a 4457 from your local Customs office. That proves you own the gun so you can bring it back into the US. The experience of getting a 4457 from CBP can be frustrating depending on where you live. The officers where I live make it difficult but others in the mid-west report the officers as being friendly and helpful. Call ahead and ask about their procedure since you have to bring the gun for inspection. Usually they are at an airport so be clear on how they want you to handle bringing the gun.
I suggest you contact Travel Express at
travelexpressagency.com
They specialize in arranging international travel for hunters and will handle all the details. I've used them and they are great.
One caution. Hunters traveling to Africa through London have reported many instances of guns being intentionally damaged, delayed or rerouted. Good luck.
