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Qf2!
Qf2!
Seems to win cleanly and comfortably. 1…Rae8 looks good, too.
Qg4
Qg4
Nice idea, aiming to line up a battery on the long diagonal, but White just chops it off with 2.fxg4. Black can win back some material (e.g. 2…Bxg2+ 3.Kg1 Bxf1), but a queen is a queen. If 2…Rxg2, 3.Rcf3.
1Qf2 Rg1 2Re1
1…..Qf2
2.Rg1 Qxg2+
3.Rxg2 Re1+
4.Rg1 Bxf3#
1…..Qf2
2.Rg1 Qxg2+
3.Rxg2 Re1+
4.Rg1 Bxf3#
That’s not mate. In fact, 5.Rxf3 looks, shall we say, promising for White.
The move you wanted after 1…Qf2 2.Rg1? was 2…Re1 and mate next move.
1…..Qf2
2.Rg1 Qxg2+
3.Rxg2 Re1+
4.Rg1 Bxf3
5Rcxf3 1-0
1…Qf2
2Rg1 Re1 0-1
Qf2
Qg4 and Qf2!