++ on using wood to support from below. Of course the door panel needs to off to get access for this, but you'll probably want to get that panel off anyway to see what is wrong. Depending on what wood scraps you may have, just make sure nothing will shift once you put them in there and it will be as permanent as you want.
On what actually broke, the rear is similar to the front, except:
- only one window clip and regulator clip per window on the rear, vs. 2 on each front window
- rear window clip is slightly different vs. the front due to a slightly different spacing from the bottom edge of the window glass to the hole the window clip goes through. I have another post on here somewhere with details - something like a 4.5mm difference that can be shimmed if you really need to use a front window clip on a rear window.
- the cable attaches differently to the regulator clip on the rears = two cable ends with spring loaded ferrules attach to the one regulator clip.
But you really don't know what is broken in there until you open it up. Could be window clip, regulator clip, or the regulator itself (cable, plastic parts, ...). In my experience, even the Genuine BMW window clips will not survive removal and reinstall, so you'll definitely need a new one of those.
If you have the window shades on the rear side windows, there is an extra step required to remove the vertical pillar thing. And there is a trick to it that I always have to look up to find - you need to pry a locking thing at the top of the pillar, and you either lever it up or down to get it free, and whatever I do is always wrong until I look it up. Possibly related to quantum mechanics, I'm sure.