Welcome to TRS
Unfortunately you can't use it in a 1993
1985-1994 Ranger used A4LD automatics, they had 1 or 2 solenoids and a Neutral switch above shift rod, also speedometer cable hook up
These years also used the EEC-IV 60-wire computers
1995-2011 Rangers used the 4R and 5R automatics with 4 solenoids and DTR sensor on side of shift rod
These years used the EEC-V 104-wire computers
These were all the same transmission as far as rotating part in the main body but have different valve bodies, and you can't swap in older valve body to newer transmission
The 1993 computer can't run 4 solenoid transmission
2003 computer can't run 1993 3.0l engine with distributor(3.0l went distributorless in 1995)
Sell the 2003 5R44E automatic and use that money to repair the 1993 A4LD
You are limited to a 1991 to 1994 A4LD from a 3.0l 2WD, as as replacement
1991 was the first year for 3.0l's in Rangers
Just FYI, losing reverse in an automatic usually means a loss of pressure to hold Reverse, it requires the highest pressure at 150psi
Forward gears just require 100psi to hold
You can often replace valve body gaskets and seals and you will get reverse back
Not always
A transmission shop can do a pressure test(or you can) to see if its a pressure issue or a mechanical issue