Any heads will need to be boiled out, clean, and bleached. Capes will need to be dipped and fixed, salted. Both will need to be tagged with your name.
You will need a freight agent capable of handling the goods, in the UK.
Trophies will need to be boxed in air craft grade timber boxes. Paperwork must contain the relevant information about the contents, full common name, scientific name etc.
Trophies entering the USA, must go through a designated port of entry for USA fish and wildlife. They can be collected from there, or the sender can arrange to forward them onto your address.
Be aware, this is NOT a cheap process these days. I sent a consignment about 5 weeks ago to New York, freight collect. The cost was £1500. Although USA Fish and Wildlife, would not release the trophies as they couldnt understand the scientific name for Red Stag (Cervus elephus) and kept asking if it was a Barbary Stag

.
In the end after about 2 weeks, and a rather stern Email from me, they realised Barbary Red Deer are from Africa (Atlas Mountains) and the customer collected his trophies.
One word of advice. If two of you are hunting, make sure you put the trophies under ONE persons name. USA customs don't take too kindly to mixed trophies in one box.
I have only just returned back from the highlands with clients, some of whom were from the USA. I have their trophies ready to send in the next few weeks. They will also go through New York (JFK) under the same process.