Sorry, I don't know what a double screen board is?
Basically it can be any board to seperate the two hives but with holes in it, holes covered with screen on both sides so they can't sting through. You want the unique smells of the hives to mix so the bees of both hives are familiar with both.
Mostly split the bees between hives, they both need the different types. The old hive still needs nurse bees, and most of the forager bees will return to the hive in the old position. The nurse bees in the new hive can quickly take over any foraging necessary.
If you don't want another hive, kill the old queen before finally combining to eliminate the chance that the old queen would kill the new queen.