If the ratio is different, you will, of course, have to replace the pinion gear as well. And that's where things get tricky with measuring pinion depth, crush sleeves, etc.

If the same ratio --- measure backlash BEFORE you pull the old diff. Pull axles/ pull diff. Hope like hell you don't need a case spreader to get it out. Install the new diff and check backlash. If you get lucky and it's the same, that puts the new ring gear right where the old one was. IF you don't get lucky, you'll have to pull the bearings off the diff that came out -- keep shims separate and together for each side. Remove the diff you just put in (and hope like hell that you don't need a case spreader to get it back out) and pull the bearings/shim packs and check them to see how they compare with the shims you removed. You may be able to replace them with the ones that came out of your old diff -- each installed on the same side. Then back in the with the diff. If you're lucky - backlash matches, you're done. If not -- make note of backlash and see which way you need to move things to get it back where it was. Pull the diff yet again (and hope like hell you don't need a case spreader), make appropriate changes to shims and back in - measure again. Rinse, repeat. Best to have some replacement bearings on hand. Not uncommon to tear them up trying to get them off.

And this is why if it's the same axle out of the same type car, it's easier to just buy the whole rearend and swap it in.

I mentioned the wiring because I had made an inquiry some months ago regarding using an '89 stick shift rear in a '93 auto body w/V8 and the answer was I could use the '93 speedo but had to switch two wires around.
I didn't realize my 940T had the lock-up till I tested it in gear with one wheel jacked up to check for rim straightness after the car was totaled while parked. Amazingly the rim was straight and all the doors worked--the rear of the car was destroyed. I guess the diff worked--I never had a moment's issue driving in wet or snow. -- Dave