According to the information I can find, the rear bumper cover for 5th Gen Celica's are different between narrow and wide body versions.
The wide body rear bumper cover is Toyota P/N 52159-20921
The narrow body rear bumper cover is Toyota P/N 52159-20920.
I don't know why there is a difference, but they are different part numbers here in the US, Europe & Australia. Japan has it's own unique rear bumper cover part numbers. You may have to be more specific regarding where your friend's ST185RC was original built and sent to, and the same for the narrow body donor.
I actually have a narrow and a wide body in my garage, and from what I can see, they look very close, but I think the rear fender angle behind the rear wheels are different and the bumper is made to match those angles, so that may be a problem in the plan you described.