relocating often has a very low success rate, I don't know if beaver is any different.
I would think it would work best, or not at all, unless you had an old pool or low pond with no inflow except when it rains. Also no out flowing water at the time of release. Release two at the same time. Do your relocating just after mating. Here that is late November or the first week in December. The no ingress or egress holds them and gives them time to adjust.
It usually starts getting a wet winter in December.
Then go back and catch them before they have their young and open the flow as it was before the release.
Hunt ducks in the pond from the sorghum you planted in July in the dry bed at the head of the pond and its dry low banks.
As long as you caught the beaver out after hunting, your not hurting other landowners.