Does someone have a definite answer to this question?

Player A and Player B are playing a blitz game for sizeable (at least
- to them) stakes. Player A has the piece in his hand to make the
mating move, when Player B calls his tiime down (before he can
complete the move). Who wins? An Eastern European spectator said that
in "his country" you were always allowed to "complete" the mate. I
would say no - Player A did not "complete" his moves in the required
time. If the spectator is right, this could mean that if a player
wanted to delay a tournament for some reason, he could hold the mating
piece in the air for as long as he wanted without making a move (he
could never lose on time). (let's say he wanted to see the result of a
nearby game before proceeding to play his next opponent)

I can't find the "Eastern European" rule on the FIDE site - or any
other sets of blitz rules that I checked. Who wins? $4 rides on the
result.