Answer juged false but who is a faster solution for probleme 22212

Hello,
thanks for this chess plateforme

I would like to notice you an answer juged false but who is a faster solution for probleme 22212

your answer is
Bf7! - Kxh7
e8=Q - Rxg8
B6! - Kh8
Rh7#
4 plays to mat

An other answer juged false but faster is
Bh7 ! - Kxh7
g8=Q! - Kh6
Rh7#
3 plays to mat

Bh7 ? - Kxh7
g8=Q - Kxg8

?