white to move... what do you do?

hi, i just finished a game playing my coworker; we got an argument whether or not after move 39...Ne3 Nc7 would be winning for white? he says that he saw something and therefore didnt play it; i saw it after i click submit(crap)and got lucky i guess 🙂
peace out
Game 4733170

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When you say g7 do you mean a7? And after 43...Kh4 does 44.Ng1 go anywhere?