Are you saying you want to mix and match ring and pinions? If yes, then that's a no no for sure. If you do mix and match a ring with different pinions, then it won't last long.
It sounds like you just want to move the posi from one rear to another. Assuming that you have two rears, one with an open carrier and one with a posi - the easiest way to use the posi is to just swap the posi into the housing that has the gears that you want to use. Most likely, repeat most likey, if you could get away with the same carrier shims as were in the original rear with the open diff.
I've done what you're trying to do many times. The best way to do it is to grab a shim kit, 2 side bearings and races. You can reuse the ring gear bolts if you can confirm they aren't stretched (remember - left hand threads.)