One of the Mini gearboxes most sought after is the late 4 synchro remote box that has close ratio gears. The most certain identification is done be inspecting the laygear. If it is a 22G1040 laygear you have a close ratio box. While you are inspecting the laygear be sure to check the inner surface of the laygear which serves as the outer race of the layshaft bearings. This surface can breakdown resulting in premature failure of both the bearing and the shaft.
These laygear are getting harder and harder to find. It is best to call to check availability.