In chess there is a situation called Drowned King "and it occurs when the player whose turn it is has no legal moves to make and the king is not in check.
That is, the king cannot move to other squares because it would be in check position or because they are occupied by own pieces or pieces that are defended, and also the player has no other pieces that can move or capture opponent pieces. This is also known as a stalemate" (Wikipedia)
In this occasion White plays and for the next move Black has no move so if the move made is not correct a game that seems to be won would become a draw.
So you must allow Black to play, there are several ways but only one would end in mate in two moves this is.
Move the rook to the A1 square so that Black's only forced move is to take the rook with the pawn and then the white queen would take the pawn which on reaching the last square has already been crowned, giving checkmate.
In annotation
Ta1 - P xTa1
Dxa1++