Reverse Puzzling 8 - Another Chess One with an Allumwandlung

[Continued thematically from here]

George grinned at the sight of the chess board. "What have we here?"

"This was the first two-mover to show Allumwandlung using only this many pieces," I explained.

"Allum what now?" It was rare to flummox George, but before I could answer he said, "Oh, I guess you're going to promote that pawn into different pieces."

"You got it. This is the first one: White to play and mate in two."

George studied the board for a moment and then said, "f8=♗, and it's mate next move. Only one line."

"Now for the second one," I said. "Back to the original position and move the white queen to a7."

Again George took just a moment: "f8=♖, and it's mate next move. Only one line."

"Now for the third one," I said. "Back to the second position but move the black King to c6."

George was in the swing of it now: "Easy. f8=♕."

"Very good. Last one," I said. "Back to the third position but move the white King to c4."

As you will have guessed, this was answered by f8=♘.

What was the original position? Bonus points for the original author of the puzzle.

Tip:

Work backwards...

• Guessing, promotion to a knight might fare the only advantage over promotion to a queen.
– humn
Apr 14, 2022 at 17:19
• @humn, there are circumstances where promoting to a Bishop or Rook is better. This puzzle provides these examples. It is a "good" puzzle in the sense that there is only one solution for each of the four variations. It would be artificial to promote to a B or R when promoting to a Q would also win. In other words, each promotion is the only way to solve the "mate in two" part of the puzzle. Apr 14, 2022 at 21:14
• Is "mate in two" invalidated if it's mate in one? Apr 21, 2022 at 1:32
• @Ausername, yes. It must be mate in exactly 2. Apr 21, 2022 at 19:15

Original Board State:

FEN: 8/5P1Q/4k3/8/4K3/8/8/8 w - - 0 1
After ... Kf6, white has Qf5#

After moving White's Queen:

After ... Kd6, white has Rf6#

Note:

In both of the previous two positions, promoting to a Queen is stalemate.

After moving Black's king:

Pretty straightforward checkmate

After moving White's king:

After the only legal move, ... Kd6, white has mate with Qc5#
Note that promotion to Queen or Bishop ends in stalemate, and promotion to a rook can only force mate in 3!

• Excellent. Only a minor correction on the first position. Qg7 is not mate because Ke6 May 3, 2022 at 21:46
• Oops! Good point, it seems I got this correct for the wrong reasons - editing now for posterity, thanks for the catch! May 5, 2022 at 18:15