Plum is right. Replacing the center differential is fine.
However, there are some things you'll want to consider before just slamming the used one in.
You'll probably need to reshim the carrier (to the left or right in the pumpkin) and make sure your backlash and everything is straight. You should expect .008" - .012" between the ring gear movement and the pinion gear. For this, you'll need a magnetic base holder to hold a dial gauge to measure this. Marking compound (to check your wear pattern) and a shim kit will be needed.
Another wise idea is to get new carrier bearings. You're already here, so why not. The original bearing races (cups) should also be used. You can get away with using used bearings, but use your best judgement: if they're too loose or out of tolerance, get new ones instead.
Make sure the clutches in the pack are good. Assume that they are worn. I would replace the clutch pack.
If you drive on the street, this is a good option. However, if you occasionally go off road or are putting a lot of poewr to the wheels, I'd go with an automatic locker instead.
PERSONAL EXPERIENCE:
In my 31 spline 8.8" swap, I had a LSD and wanted a locker. I had to buy an "open" carrier, put the locker in, and check it that way. As things turned out, I did not need any shims. My original configuration was still valid with the new differential carrier/case. You might get lucky.
That being said, Plum offered to sell you his LSD for $75. I'll sell you mine for $74. (jk jk)
...but I WILL sell you my shim kit that I didn't use for the 8.8"...I think I paid somewhere around $20 +tax for it. I'll sell it to you for $18 shipped.
Just trying to help a fellow TRS-er out.
Good luck.