I'm struggling to find the full solution of a chess problem I'm starting to think that this puzzle, found on chess.com here in the 5th post down, does not have a correct full solution. But it features a nice line if Black moves wrongly, so judge by yourself.
[Title &quot;White to move and win&quot;]   
[FEN &quot;8/8/7B/K7/8/7p/4Bkp1/6Rb w - - 0 1&quot;]    

I think I have found the first move, after which black has two options, and I have found the solution for one of the two:

 1.Ba6 Kxg1 2.Be3+ Kh2 3.Bf4+ Kg1 4.Bg3 h2 5.Kb5 $3 Kf1 6.Kc5+ Kg1 7.Kc4 Kf1 8.Kd4+ Kg1 9.Kd3 Kf1 10.Ke3+ Kg1 11.Bf2#

The only problem is that black is not forced to pick this line, and could go for the other option:

 1.Ba6 h2

In which case i'm completely stuck. I've tried using a browser version of stockfish, which can't solve it either. So does this puzzle really have a (full) solution?
Yes, there is indeed a full solution. There is a move that you missed that wins for White after 1. Ba6!.
[FEN &quot;8/8/7B/K7/8/7p/4Bkp1/6Rb w - - 0 1&quot;]

1. Ba6 h2 2. Bf8!

Now, no matter what Black plays, White will play 3. Bc5 and control g1. Thus, White is able to prevent Black from obtaining a queen for long. As such, White wins as stipulated.
However, it is very understandable why one would consider the resulting position as a draw. The Shredder tablebase proves that White can squeeze out a win by slowly cutting off the Black king. It is difficult, if not impossible, for a human to even find the right ideas. Therefore, it makes sense that Stockfish can't find either, if not rather quickly. It's an easy mistake.
[FEN &quot;8/8/B7/K7/8/5k2/6p1/6Bb w - - 0 1&quot;]

1. Kb5 Kf4 2. Kc5 Ke5 3. Bc4 Ke4 4. Kd6 Kf5 5. Bb3 Kf6 6. Be6 Kg6 7. Ke5 Kg7 8. Bd5 Kg6 9. Bc4 Kg5 10. Bd3 Kg4 11. Bc2 Kg5 12. Bf5 Kh4 13. Kf6 Kh5 14. Bh3 Kh4 15. Be6 Kh5 16. Bf5 Kh4 17. Kg6 Kg3 18. Kg5 Kf3 19. Bd3 Kg3 20. Be2 Kh3 21. Bg4+ Kg3 22. Kf5 Kh4 23. Bf2#