How can one guide a person praying in the direction other than the Qibla to correct their prayer without angering them?

Directing someone who is praying while facing away from the Qibla corrects their error, and this falls under the category of changing the reprehensible and offering advice. It is incumbent upon the person to accept the advice if the one informing them is trustworthy. If the worshiper becomes certain of their error while in prayer, they should turn towards the Qibla, and their prayer is valid according to the Hanbalis and Hanafis. As for the Malikis, they differentiate: it is obligatory for him to break his prayer if he is not blind and the deviation is significant. However, for a blind person or one whose deviation is slight, turning is sufficient and their prayer is valid.