Careful though!
I did this on my 2000 Ltd and the hydrostatic pressure was transferred to the transmission, not allowing a full shift into park and other oddities. I don't think mine had even been done before, as it took a lot of pressure with a Lincoln grease gun to get any old grease to squeeze out. I had to release pressure by removing the zerk fitting. This can be done by just pushing the ball in as well.
Mine was so full of grease with nowhere to go, it was like an iron rod. The shaft is obviously in 2 pieces so it can move, so removing this play = not good!
So mine is on a long term plan. I lube it every other week or when bored, hoping the new grease will be worked in by the process of driving. I force it in there as much as I can without effecting the trns.
I read a thread somewhere where someone suggested using a thinner grease to work out the old, then followed by the proper grade. Sounds like a good idea on paper, but I can't find the thread.
I may disassemble and clean the splines if this doesn't loosen up after a couple more attempts. It does move, but obviously some old grease still in place.
So just be careful, and if you get the problem like I did, simply release pressure as above.