Puzzle on level 14 of repetition does not allow to make correct move

[link2xt]

Here is the puzzle:

It only accepts the move of king to f7 as correct. But if king is moved to f8, the solution is the same (pawn h7, then rook h6), yet it is not accepted, showing "try again".

Here is a lichess analysis board if you want to try: https://lichess.org/analysis/8/4K2k/5R1P/6P1/8/8/8/8_w_-_-_0_1
Stockfish also proposes only one solution, but if you move king to f8, evaluation does not change (white win in 100%) and it continues correctly. Is it a bug in stockfish analysis that propagated into blitz tactics? Why is there only one solution?