Black captures have been e7xd6xc5xb4xa3 and d7xc6 accounting for all 5 captured White pieces. White's 4 captures are hxgxh and fxgxh. White cannot retract b3-b4 before reconducting the wQR home. Hence he has only a few pawn moves before he is retropat. Bl. must free Wh. quickly with the retraction of d7xc6, but he must reconduct the bRa8 and the bBc8 before. These must be uncaptured by the wh. Pawns.

There is only one way to do this fast enough, e.g.

-1. g7-g5 g5xRh6
-2. Rd6-h6 g4-g5
-3. Rd8-d6 f3xBg4
-4. O-O-O f2-f3
-5. Bc8-g4 Kb5-a5
-6. d7xRc6+ etc.

Last move was g7-g5 and White wins with 1. h5xg6 !