Thank you all for help!
Shifter is Syncro II, without the micro adjusting knob. The "mushroom" was fitting on the round part of DT boss, but not on flats.
I cleaned the flats, there were no paint or anything notable. I thought that I will file just the "mushroom" part and not the boss because if I'll ruin it , it will be the easily replacable shifter, not the boss.
So, after 30 mins of careful filing and checking I got the part snugly on flats, the rest of the shifter went on just fine, so shifter is in working order now
