The Cortina box is the lighter duty BorgWarner used behind 3.3 Falcons in the XE. It was used in Sigmas, Datsun 200B,Commodore 4's and 6's and RWD Coronas in modified form. The Cortina 4-spd gearbox is 5" to far forward in the gearshift when plonked in a Falcon. Ok if you have a bench seat!
All the ratios are the same as the European Cortina, with 3.65, 1.97 and 1.38, and 1.0 tops.These numbers pop up with the Aussie made Sigma, Datsun 200B, Commodore 4's and RWD Coronas. As a five-speed, it got a 0.85:1 top gear.
1982, Ford oz saved a massive 9 kilograms by using this smaller single rail, and shoved the Commodore 4 gearbox behind the 3.3. It had a reworked mainshaft with 3.22, 1.94, 1.26, 1.00 ratios as a 4-speed, and 0.79" in overdrive fifth. If you can get a linkage to suit, the Cortina gearbox drops in behind a 4.1 or 3.3, but its life span will be very short. Even running ATF, the 3.3 5-speeds were very prone to syncro and mainshaft failures.
A point worth noting is that the first gear was too tall on the early XE's, and Ford changed it to a wider ratio 3.47:1 first by the time the XF rolled out. Still a crap trans. Never made for anything but a stock engine tootling.