The factory trans in 1983 would be a T176(4spd) a T4(4spd) or a T5(5spd), so yes your trans is a replacement.
As to what 3spd it is there are many possibilities.
The T150 (3spd) was used from 1976-1979 so that is a good bet. However the T176,T4 & T5 all would be mated to a Dana300 xfer case, while the T150 & all 3spds prior to 1980 would be mated to a Dana20 xfer case. Funny how with Jeeps every answer leads to another question.
The Dana 20 has a short shift lever that is far to the passenger side & almost under the dash(a strech to reach from the driver seat while buckled in).
The Dana300 has a straight shift lever that is about 12-15inches long & right next to the trans shifter.