[Bigdav160]

Did you mark the caps? It's critical that they go back on exactly how they came off. Top/bottom Left/Right.

Pry the ring gear and case out. Keep track of what shim came out of the left and right.

Unbolt the ring gear. Look at the bolt head. Does it have an "L"? Left hand threads. Tap on the edge of the ring gear with a brass drift. Or thread the bolts on half way and gently tap them until the ring gear comes off the case.

Make sure everything is spotless clean. Bolt it to the new case. Torque the bolts
Install the case with old shims and check the backlash. If the backlash is good run a pattern check. Most likely it'll be acceptable.

Pinion depth does not change with case replacement.