If you checkmated him you would simply win. If it's his move and he leaves in Live chess, you would win the game by abandonment, and if it's online chess, you would win on time. Just make sure in live chess you wait for the box to pop up saying you won or it might take it as you quitting. I hope that answers your question.
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If I checkmate my opponent in my next move and he just leaves the game without resigning what happens concerning recording my win?