If this Muslim is exempted from fasting, this is permissible but one must not do that especially if this hurts the other Muslim feelings.

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This is not permissible, as each woman must have her mahram with her.

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It can be done in other months and it can be as little as a day or more.

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No, and why would you want to do such a thing?

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Yes, provided she goes with a mahram and that she had already performed her own Fard hajj previously.

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