The first observation is that white's h1 rook was captured on c6. So, how did it get there? It had to have been captured BEFORE black's a8 rook. That means, black's dark-squared bishop was the first piece captured.
Of course, we all know what this means. For the h1 rook to escape, the f1 bishop can't be in its current location, and yet it cannot move with pawns rooted on g2 and e2. Therefore, the f1 bishop is an illusion- it was captured by a black knight.
EDIT: Sorry if I wasn't too clear. Black's dark-squared bishop was captured on e3, opening the f-file, which can only be used if the f1 bishop is gone, and as it can't move at that point it must have been captured.
There is an officer on the board that is in fact an illusion. Knowing that the royalty has neither under attack nor have they moved, figure out which piece is not real.