I have a few of both versions of boxes apart on the workbench at the moment so I measured the diff units.
The UN1-13 2-spider diff unit is 83.5mm from the bottom of the diff where it sits against the crownwheel, measured to the inside bearing surface by the output shaft. The same measurement on the 369/5 with a 4-spider diff is 79mm. On this particular box I have to strengthen the diff on, is to put the 4spider unit into the -13 2spider box. But it required a spacer plate of 4.5mm to do this. In your photo you cant see the rear of the bearing mounting surface, so you will just have to do your best with a small straight edge and vernier and eyecrometer to measure, but you will get a good idea anyway from that method.
If you have a look on the sides of the crownwheel it usually has the model stamped or engraved on there.
The swap would be straight forward as the 369 and UN1 cases are the same with regards to the internal bearing mounts/distances etc. Oh and the 369 box came out of the Renault 30s and was the 369/4 was a 4-speed and the 369/5 the 5-speed. Externally (and almost internally), they look 99% exactly the same.
Just as a matter of interest have a look at the manufacture date on the gearbox casing. Its cast by the output shaft on the left hand side (passenger side for RHD vehicles) on the bellhousing mounting flange at the very front of the box.