Physically it fits, but its a mix-match of front diff ratio vs rear diff ratio = not good!! You will lock up the front or rear diffs at a certain speed and break things, so please dont do it.
To make it work, however, you have to open the EVO III gearbox up and swap out the EVO III's 63-tooth front diff crownwheel and 15-tooth output pinion with a GSR's 58-tooth front diff crownwheel and GSR specific 15-tooth output pinion. This will make the EVO III gearbox run the same front diff ratio as the GSR gearbox and therefore will be good to use with a GSR 1.09 transfer case and GSR 3.545 rear diff ratio.
Dont be fooled by the tooth count of GSR and EVO output shaft pinions both being 15 teeth. The size and shape of the teeth are different between them and they dont interchange.