Correction: the knob goes up and down when I hit the remote but the OUTER and INNER handles have no effect.

Then I read somewhere on the internet that one needs to sit in the rear seat, pull on the INNER handle and hit the remote. I did this a few times and now the doors opens from both outside and inside.

Weird, but the problem seems to be SOLVED for now!
I may need to lubricate the lock actuator later!
What is weird is: the LR door is rarely used but is the one with issues.

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1998 E39 528i 5sp MT
2006 E53 X5 3.0 6sp MT