Both are 4×4 5.9 automatics the 96 is a 2500 and the 2001 is a 1500

 

Electronics are different. You will need the governor pressure sensor, solenoid, and retaining clip for whatever year your truck is.

Going from 96 to 01 will work, going the other way won't, as the newer trans won't have the mounting points for the t-case shift lever. (which mounts to the body on the 98 and up trucks.)

 

Is the transmission out of the 1996 a 46RE? Just need to check as 1996 is a cross-over year for the transmission. I have an early 1996 Ram 2500 4x4 and it has a 46RH transmission.