As already mentioned, Evo 1 to Evo 3 trannies will fit in a GVR4. However, in order to use them in a USDM GVR4 a couple of other important considerations not mentioned thus far must be taken in to account:
1) LSD factor -- It is important to note if your Evo trans has a standard or LSD front diff. The former will work no problem so long as you address the rear diff (or trans final drive) issue already mentioned. HOWEVER, unless you have the correct front inner axle cup on the passenger side, there is no way to use the LSD gearbox as is, and to make it work you would have to convert it to a non-lsd or swap in an aftermarket LSD that won't require the special axle stub.
2) Starter plate reminder -- If you are using an Evo trans, be sure to use the correct starter plate. This is determined by the type of tranny bell housing that is used, a GVR4/1g or Evo/2g type. NOTE: I am not sure if all Evo 1 to Evo 3 gearboxes have the same bell housing design (Aussie/NZ guys chime in please). I learned the hard way that the bell housing of an Evo 3 trans is a 2g type (as 3rdstrikedsm points out). I lost a tooth on a flywheel and had loud grinding noises upon start up due to the slight misalignment that resulted when I installed it in my GVR4 with a GVR4/1g starter plate. After I dropped the trans, changed the flywheel, and swapped in a 2g starter plate, I was off and running.
3) Transfer case compatibility -- It could be that the issue goes away if you use the right trans with the compatible rear diff. I use an Evo 3 tranny (UPYE) + USDM tc + Evo 3 rear with no problem at all. This is not supposed to work but it does. Could it be that I am unknowingly using the later (97-99) 2g tc? Is there any way to check this visually without removing it?
Also, a buddy uses a non-LSD trans from a GVR4 RS (WQNK) + USDM tc + USDM 3.545 rear diff converted to 3.909. [He converted the rear diff by swapping in a 3.909 ring & pinion set he was able to purchase at the time (no longer available).] Another local guy uses an LSD trans from a GVR4 RS (WQFE, with the correct inner axle stub, no longer available from the dealer/MMC) + USDM tc + GVR4 RS 3.909 diff. Will the Evo 2 trans (LSD or not) + USDM tc + 3.909 rear work? It has slightly different gearing than the Evo 3 and Evo 1 tranny. Based on the experience reported by local and forum GVR4 owners it would appear that it would.
As to your trans, it is from a JDM GVR4 RS and it would work with a 1g tc (or pre 97-99 (2g) or USDM GVR4 tc) and the 3.909 rear diff. However, since it is an LSD gearbox, as noted, you must find the correct axle part to use it.