K. Stempel  White retracts last move and then mate in 1. White missing pcs: Q, Pa =2 Black missing pcs: Q,R,R,N,N,Bf8 =6 Captures: White Bc1 never moved and was captured on c1. Therefore Bg7 is promoted from a-pawn. The only possible promotion square is f8 via a2xb3xc4xd5xe6xf7-f8=B. So a-pawn captured all missing black pieces -except Bf8- on white squares. Bf8 was captured separately by a white piece - not pawn, which would result on doubled pawns. The only black capture has been d7xQe6, which has happened after the last white a-pawn capture e6xf7. Thus all captures have been explained. The last white move could not be a capture or if it was, then it was a capture of Bf8 by Nf8,Bg7 or Rh4.

The Analysis: The problem here is to provide a legal last move for black after white's retraction.
 In the diagram position theresimply is no retraction for black. Any pawn move retraction will result in illegal position.
The only king move retraction Kf5-e4 steps into irreal check.

So how could white retract a move so, that black has a last move,too?

Could it be one of the captures Ng6xBf8, Bh8xBg7 or RxBh4? Alas no, as in all cases the uncaptured bishop is immobile!

What about retracting Nd7 to b8 or c5, when black can retract d7xQe6? Unfortunately this is only temporary relief, as white must
remove the queen check next (without capture) and then black is without last move.

It turns out that the only viable retraction for white is Ba8-h1. Black can then step into the doublecheck by Kf5-e4 and  white blocks
the checks by retracting Re2-g2. The resulting countercheck by Bd1 is then masked with Ke4-f3, whereafter the position unfolds.

The solution is: White retracts the move Bh1-a8 and instead mates with Bh1-e4#   Back