I've read about the "mate prevail thing" here : Mate Prevails - Chess Rule but I couldn't get a clear view on one odd point.
I get that the mate move prevail, but if you couldn't do it before the fall, you lose.
Let's say it's my opponents turn. I'm about to mate in 1.
He hits the clock, I run out of time.
Then he notices it, and claim it when I'm performing checkmate (the exact same time).
Note : If needed I'm talking about FIDE rules