I have just finished mine on an 88 also, but i have no lift, yet...
I don't have part numbers sorry, just hit your trusted auto parts stores ahead of time.
You will need U-bolts, i picked mine up from NAPA, had to order them in took 3 days is all, you might want to check on this before you start.
The Plates off my 35C went on the 44, it was tight but they worked, be careful of the threads, but they should be no problem.
The drive shafts are not the same length, the 35C is a bit longer, i heard 5/8 some say up to 3/4 of an inch. I had to go get a 8.25 driveshaft, but i have no lift as i stated, when i did research on this forum i found many posts conferming that even a small lift was good enough to clear the extra length, i think you'll be fine. I thought mine was okay, it wasn't mine ended up rubbing the rubber ring on the T-case seal and when i went to tow a small trailer (1300 lbs) it tore it off, probably lucky i didn't do worse. Again i had no lift, stressing just check this.
Get a new pair of U-joint straps for the 44, just replace them now while your under there. Or if you feel up to it search and find the tech on drilling the 44 yoke out and go to the u-bolts for the yoke.
The 44 has a different axle vent than the 35C, but it's no big deal just a relocation, make sure the 44 has the nipple on it when you snag the axle or your going to have to go get a replacement.
Your brake cables and all the rest of your hardware should work flawlessly.
That all the tips i have for now, it was a fairly straightforward swap just because the axle came directly from another XJ which makes this an easy improvement.
Andy