Problem with puzzle

http://en.lichess.org/training/47534

I started the line by Bxg5 Kg7 Be7 Kh8

the line the tactic gives is Bxf8 c5 Rg8# however there are two other valid lines.

after Kh8 you can play:

Bf6+ Rxf6 Rg8# or you an also play immediately Rg8+ Rxg8 Bf6#

oops you cant play the second line Rg8+ Rxg8 Bf6# because it leads to check on the king, however the other line is valid

The second line is wrong, as you said. The first line is accepted by the website as a valid solution. I don't see any problem with the puzzle.