Unless someone changed it, it came stock with a Peugeot BA10/5.
Very weak, and expensive to repair... I know first hand, and should have followed advice of others and NOT PUT ANY MONEY INTO IT.
But the AX15 is nearly a direct replacement, depending on year and a few details.
I have an 87 that I bought a AX15 with NP231 from a 92 or 93 Cherokee. I had to buy a new clutch disc, make a new trans mount, reman the TC linkage, transfer the speedo housing (from electronic to the mechanical, direct swap from the BA), and re-clock the transfer case. Also some minor body massage for the shifter, but its also got a 4" lift which amplified that problem.
If you do a search, you can easily find out what years, and what to expect in the swap. Of course that is assuming it isnt already an AX15. If you go here The AX15 Transmission - Novak Conversions
they give you a good idea of what to look for if its already been swapped. Do a search on the Peugeot BA10 to get an idea of what it looks like, but basically the BA10 does not have that cast aluminum mid plate that the AX15 has making it easy to determine.