Not pressing Clock - Query on law of chess!?

In a game with increment or time controls (40 moves in 90 minutes and next 20 moves in 60 minutes etc., assume player A makes a move but forgets to press the clock and player B doesnt notice it, thinks for some time and makes a move. Now he realizes opponent hadn't pressed the clock.

Now does this constitute an illegal move by player A if claimed by B? Wouldnt this cause an issue say when you make the 40th move (the clock will reset to the new control only on 41st move since it was not pressed once in between?) or basically there is lesser time for both since increment didnt happen for that missed move. It would be nice if someone knowledgable could help clarify this. Thanks.