This is a tough problem. In at least one of the side variations that arises at move 8 for black, it is enough to reduce the position to a winning position according to the Nalimov Tablebase since I considered that line inhuman (the composer didn't discuss that line at all in the solution he offered). The denouement of the main line is understandable, and is 13 moves deep, and is quite amazing by itself.
1.Nb6+ Kd8 2.a8=Q Rxa8 3.Bh4+ Kc7 4.Nxa8+ Kb7 5.Be1 Ne4 6.Bg6 Nf6 7.Bh4 Nd5 8.Bf7 Nb4 9.Be1 Nc6 is the main line, and the most interesting one.
Alena, the main line is 9.....Nc6. The main variation in your line is at 8....Nf4 instead of the mainline's 8....Nb4. 8....Nf4 is the inhuman line I mentioned above.
1.Nb6+ Kd8 2.a8=Q Rxa8 3.Bh4+ Kc7 4.Nxa8+ Kb7 5.Be1 Ne4 6.Bg6 Nf6 7.Bh4 Nd5 8.Bf7 Nb4 9.Be1 Nd3 10.Bd5+ Ka7 11.Bc3 Bb7 12.Nc7 Nf4 13.Nb5+ Ka6 14.Bxb7+ Kxb7 It's a winning position for white.