@t3p3tony - The day before yesterday, the new ordered parts arrived. In the meantime, I made a completely new wiring to the MFM, re-soldered the connector (for safety) and the problem persisted.
After replacing the MFM control board, everything works without problems. Already the second 20h print and not a single fake filament alarm.
m591 d0
Duet3D rotating magnet filament monitor v3 on pin 121.io1.in, enabled, sensitivity 24.80mm/rev, allow 75% to 125%, check printing moves every 5.0mm, version 3, mag 133 agc 95, measured sensitivity 24.82mm/rev, min 96% max 104% over 31549.8mm
It really worked out for me to record printer on camera and see what happened after stop print. Just such an idea once someone solves a similarly strange problem.
Thanks to all for help.