I'm sure there are much better experts on this site than me, but I'll take a crack at giving you an answer.
After you have taken an animal, your PH will ask you how you want to preserve the trophy. This is where you tell him if you want a full shoulder mount, just the skull for a European mount, want a full flatskin, save the backskins etc. He will then let the skinners in camp know this and they will do the initial prep of the trophy to keep them from spoiling in the short term (usually salting hides and cleaning the skulls). They will only save the parts that you tell them too, so it is a good idea to have some sort of a plan before you get to this point.
Once your safari is done, another company will come and pick up (or you outfitter will deliver) your skulls, skins, hides, etc. This company will then go through a process called "dipping". This encompasses several steps in which the skulls are boiled, dried and "dipped" in a solution to kill all bacteria. The hides are also "dipped" in a solution and then salted for a long period of time to kill any bacteria.
After the skulls, hides, etc. have been "dipped", they will then be "packed". This basically means they are wrapped in bubble wrap, put in thick plastic and then crated up for shipment to the final destination.
Hope the info helps. Also, if anyone with more knowledge and experience than I has a correction please set me straight.
As far as what the best way would be, I would suggest having your trophies "dipped and packed" and having your taxidermy done in the US. Talk to your taxidermist before you leave and get some tags from him that you can have your PH put on your trophies for additional identification.
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