I also use a large Williams trap to relocate snared beaver. But I do it a little different than Jim. I first unhook the beaver from the anchor and pull him to a level dry working space(if one is available). Then I take the anchoring end of the snare and run it though the open upside down trap and thread it through the back mesh. Now all you have to do is pull the beaver into the trap, or push/slide the trap down the snare over the beaver. Finally invert the cage so the door closes and locks. For removing the snare I reach through the cage with pair of long needle nose pliers, and grab the loop near the lock, give it a good pull and it will usually release. If the kock does not release pull the loop up to the side of the cage with the pliers and cut it off with a good pair of side cuts or cable cutters.

The only reason I can think of to relocate beaver would be something of great angst. ( This would include a neighbor with an Obama sign or someone who stole your girlfriend; the guy who stole your wife has enough trouble already )

I actually did relocate the second largest beaver I've ever caught to a friend who had a zoo. ( And orders for live beaver ) That beaver ended up in a zoo in Green Bay. ( The last I heard he had beat out several defensive backs for a starting job on the Packers ) As good as their defense was last year, I don't doubt it.