Is there a consistent transcript of the chess game between Sherlock Holmes and Moriarty?

At the end of Sherlock Holmes: A Game of Shadows, Sherlock Holmes and his adversary Professor James Moriarty engage in a blitz chess game, which morphs into a game of blindfold chess while they are reiterating the major plot points of the movie (both past ones and current events elsewhere in the Reichenbach castle and in London).

I was wondering if this was a genuine chess game and if there is a complete transcript (i.e. all moves) of the game. Or was it just random moves without a consistent progress to them? What we see/hear in the movies:

1. Moriarty (playing White) opens with 1. c4.
2. We see Holmes playing ... d5 while he already has a pawn on e5 and no other movement on the kingside.
3. Next, we see that White has played g3, Nc3 and cxd5, Black has played Nf6 and we see Black playing Nxd5.
4. White plays Bg2.

This is all we see of the chessboard in close-up. A more or less plausible move order would be 1. c4 e5 2. g3 d5 3. Nc3 Nf6 4. cxd5 Nxd5 5. Bg2; it's uncommon for Black to play d5 so fast in this opening but it's not immediately losing. Also, the 1. c4 opening became mainstream with the Hypermodernists in the 1920s, much later than the time in which the movie is set.

We skip the rest of the opening and resume the game at a point where Holmes and Moriarty have left the board and are playing blindfold chess, speaking moves to each other in (English) descriptive notation, which was quite common at that time:

"Bishop takes knight to check."
"King to rook two."
"Rook to kings rook 3, check."
"Bishop to rook 3."
"Bishop takes bishop."
"Rook to bishop 4."
"Rook takes rook."
"Pawn takes rook."
"Bishop to bishop 7."
"Queen takes knight pawn."
"Bishop to bishop 8. Discovered check, and incidentally, mate."

_{(italics denote Holmes/Black's moves)}

Converting to the more common algebraic notation this would be

...  Bx__+
Kh2  Rh6+
Bh3  Bxh3
Rf4  Rxf4       
gxf4 Bf2
Qxb_ Bf1 mate

Here, underscores denote unknown squares, because we don't know the position or because "King to rook two." can mean both Kh2 and Ka2. White's last move ("Queen takes knight pawn.") could be Qxg_ as well, but then it's hard for Black's move to be mate.

We also have one shot of the chessboard in the background, presumably with the position where they started to play blindfold (but with some moves missing before we get to the final sequence):

We see some remnants of the opening (e.g. the fianchettoed white bishop on g2) and the missing white h-pawn can be a critical factor in the success of Black's mating attack. So it's not unlikely they have used a real chess game for this (as they often do in movies) but I wasn't able to find it.