Discovered Defence!

I'm working through Chess Endgame Training by Bernd Rosen and came across this Rook Ending.

Can you solve it?

Exercise 12.16 White to Move (Wotawa 1952)

I had only looked at the thematic inteferrence

1. Rh5 Kxh5

2. h7 Rh3+

3. Kg2

and assessed this as winning for White, as I couldn't see how Black can stop the h-pawn

I missed Black's defence from this position