Not sure about the official procedure, but what actually happens is that you fill out all of the correct paperwork and follow procedures to apply to bring home a trophy which your unit has rightfully obtained.
Then, someone hidden along the chain tells you that trophies are pooled and allocated on a unit basis, and then voila, you top trophy is suddenly reallocated (presumably to the RMP/HQ type bod whose eye it caught). You get two tatty AK's, they get your gold plated dragonof.
Your unit QM should have the procedures. I've recently returned from TELIC and there was a policy in place that authority would not be granted for war trophies to be taken out of theatre - that said, they still wanted you to apply, presumably so that someone behind a desk in a HQ somewhere could turn your request down!