7468 - Gianni Donati
Last move was g2xNh3. A queen-move would give black no retro-move, and uncapturing another piece would result in an illegal check to the white king, or in no retro-move too.
7469 - Gianni Donati
[The diagram shows a J. Henrik Juel received the problem on an envelope, sent to him by Gianni Donati]
bBd1 is promoted, so it is tempting to try c2xd1=B+? or d2-d1=B+? as last move; but this requires too many pawn captures. bBd1 is the original bPg7 promoted on f1 or h1, and the last move was c2-c1=B+.