Re: Transmission years that will fit
The 45RFE transmission from 1999 is exactly the same as the 5-45RFE transmission from 2004. The only difference is the programming of the TCM, which adds the fifth gear. So the 2004 transmission should work well in your 2001 Jeep.
Most probably your 2001 Jeep TCM is already loaded with the newer software, adding the fifth gear, unless it never returned to the stealer after 2002.