Her husband’s father does not pray because he denies that it is obligatory; how should she interact with him?

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Check below answers in case you are looking for other related questions:
A Woman Does not Act as a Mahram for Another Woman
The wife of your wife’s father is not a mahram for you

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Related Answers:
Should she cut off her ties with her adopted brother who has left Islam (is an apostate)?
Who are the mahrams in front of whom a woman can uncover?
The maternal and paternal uncles of the husband are not mahrams to the wife
A Woman Does not Act as a Mahram for Another Woman
The wife of your wife’s father is not a mahram for you

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