Really need the whole number The auto box on that age RRC will be the ZF 4HP22.
If you RR already has an automatic box then it is a realtively straight forward swap, just remember to fit the torque converter to the box first and then onto the engine. The TC is not the same as a manual clutch.
IIRC there are also two transfer boxes fitted to the ZF if that age RR as well, the LT230 and the VC. If you do not have a diff lock postion on the hi/lo lever then you current have a VC. These are ok, but I would choose an LT230 as there are more 'rugged'.