An easier "invalid move" problem

Bh1 and g1=Q are mutually exclusive because before either move, the g-pawn would have been at g2 and the bishop would have been on the h1/a8 diagonal. But the pawn would block the bishop from reaching h1.

Bh1 and Rhc1 are mutually exclusive because before either move, the rook would have been at h1, thereby preventing the bishop from moving there.

To resolve both of these conflicts by eliminating only one move, Bh1 must be eliminated.

Therefore, of the four moves given, Bh1 is the one that is not possible.

Ng1+ is the invalid move, one construction being (in Forsyth notation)
8/8/8/8/R1Bk1B1R/2N5/5K2/B5Q1.