The following info is meant for Bseries HYDRO transmissions specifically.
In order to mix and match successfully, one must use the LSD/open diff AND the final drive (ring gear + countershaft/pinion) from the donor box before it will fit into the new box.
So in your case, using a B16A box, you would need the EK9 LSD plus the final drive before you can get it to fit into the B16A box.
Your options are to purchase an aftermarket LSD that is intended to fit your B16A box...or to purchase an aftermarket final drive (for better acceleration or taller gears) and use the EK9 LSD if so you desire.
Whatever you decide to do, don't forget to shim the diff (this process is detailed in the service manual) and change out the differential/LSD carrier bearings. It may also be a good time to inspect and change the input shaft bearing and install new axle seals.