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If he escaped to 2e then you can move your knight to c3 and then yes that is checkmate :)

The pawn on b2 is overlooked in the scenario. It would capture the knight.

For what it is worth, the game went:
f6-e3
d1-e1
d3xd2
e1-f1
d2xf2 check mate

That is a nice move as well. Taking the rook in the end. But the game ended with a checkmate in 3 moves.

The game went:
f6-e3
d1-e1
d3xd2
e1-f1
d2xf2 check mate

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