Puzzle from one of my 3+2 games. Black is down a rook. Can you find the best move? Black to play.

Q-a3

FEN of the position

Black queen to A3 and then B2 for checkmate.

White can check with the queen but as soon as black gets a free move it's over

Queen from F8 to A3? Then from A3 to B2?

I dunno, my chess ain't good.