You posted this too late considering that the solution has already been found by several players above, unless you came to this post trying to solve the puzzle first without scrolling down to see what others wrote.
In such situations castling is improbable because in the endgame stage, the king or the rook will most likely have moved.
The solution with 1...Kb2 is wrong because the move is illegal.
We all know what he meant.
With a BP added on g2, Black's last move could have been made by that P, so you can't prove that Black's K or R had moved previously. That means castling is legal here and it would defeat 1.Ra8?
Even after Bg5 castling is legal. (https://en.wikipedia.org/wiki/Castling)
White Rook can still deliver mate, but not on a8 in this scenario :
I think you meant to say Be5, in which case, thanks for confirming what I said.
Bishop e5 of course. Corrected in post above.
Point also being, you can castle even if your Rook is under attack.
Obviously.