Can a player in check win the game by checkmating his opponent with one move (a move that does not move the checked king)?
A move that does not lift the check is illegal. So, if this move does not lift the check, then: no. However, the following could happen: the player can take the piece that gives the check and mates at the same time. Consider the position above. The white queen can take the black rook, thus lifting the check and giving mate at the same time.
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