Ok so I am officially very proud of myself now
I assume this is the line that cashgomer was looking for:
1. e7! Nf4+ (the only move) 2. Qf4 h1Q 3. Qa4+! Ka4 4. e8Q+ followed by mate. I was a little frustrated that I did not find this faster as it is not that hard. However, after looking at it more, I thought: "what if black does not promote immediately but gives a check first?" I am not sure whether it was intended by cashgomer's friend (i assume it proly was) , but that's where the really sick line is. I quadruple-checked and I think it is all forced.
1. e7! Nf4+ 2. Qf4 Qh7+ (in order to disturb a matting pattern where king is needed on d3) 3. Kd2!! (3. e4 blocks queens access to a4 square) h1Q 4. Qxa4+ Ka4 5. e8Q Ka5 6. Qa8+ Kb5 I reached this position and could not find mate for a while, but my experience in problem solving told me that this HAS to be a correct line and there has to be something here and then it dawned on me. 7. Nc7+ Qc7 8. a4+!! (Qxh1 is probably losing because of black's super strong g-pawn) Kc4 9. Qg8+!! Qd5+ 10. Kc2!!! Qxg8 11. e4!!!!!!!!!! and the mate is unavoidable.
Wow, what an incredible problem that was, I am not at all sad for spending 30+ mins on it. Fantastic geometry