Is it permissible to say "Yarhamukallah" (may Allah have mercy on you) to someone who sneezes if they do not say "Alhamdulillah" (praise be to Allah) or if their saying "Alhamdulillah" is not heard?

One who sneezes should praise Allah the Almighty, and one who hears him should say to him, "May Allah have mercy on you," provided that the sneezer has praised his Lord. If he does not praise Allah, then he should not be responded to with "May Allah have mercy on you."