Reverse stopped working, 2000 BMW 323i

[Yober]

Couple days ago when I tried to drive in reverse my 2000 BMW 323i suddenly the car did not move back and it felt like the gear is in Neutral position. I drove forward for several kilometres then switched off the car and tried few times shifting the speed lever from P to D2. Then turned on the car and luckily the Reverse worked.
Today the same happened again, i. e. when I arrived home and tried to park the Reverse speed didn’t work (feels like the gear is in Neutral position). Tried to shift the lever from P to D2 but unfortunately this time I could not make it work.
When I shift the lever from N to D I feel the gear is working. When I shift from N to R I don’t feel any mechanical movement in the transmission.
What can be done?

[MarcoZandrini]

The first step in diagnosing a problem is to scan the engine computer (DME) and the transmission computer (EGS) for codes. The second step is to check the transmission fluid. BMW sourced automatic transmissions from GM of France and ZF of Germany. The fluid pan on the GM box has smooth sides. The fluid pan on the ZF box has ribbed sides. They take different transmission fluid. The GM box uses Dexron3 and the ZF box uses a more expensive fluid. Make sure the correct fluid is put in the transmission.

[Raddee]

Best case (you have a GM box): it's likely your lockup solenoid broke up and the pieces are now clogging up the reverse gear in the valve body. You can replace the lockup solenoid and clean out the valve body and have a working reverse again.
Worst case (you have a ZF box): your reverse drum has broken to pieces and you should start looking at getting a replacement gearbox.

[Yober]

I looked under and see that the trany’s tray has smoth edges. So I guess it is GM brand. Also my car was made on 09/1999 and according to Bentley info and Transmission Charts all 323i cars made before 03/2000 came with GM transmission.
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I went (without my BMW) to Stan’s Transmission and the rep told me that there is no point to scan because the scanner wouldn’t show any codes. Also he said that if the cause of the problem is the reverse solenoid ( or properly called pressure regulator lockup clutch) , then it means that the screen inside of this solenoid broke off and traveling somewhere inside the valve body causing the blockage when reverse speed is engaged. He roughly estimated about 3 hours worth of labor plus the parts (solenoid, gasket, filter and fluid) all tougher around $800 CAD. And he doesn’t guarantee that this is just the lockup clutch issue.
I think I can do it myself. All I need is DYI detailed instructions.
Does anyone have the R&R for replacing the lockup solenoid ?