If a woman wears her headscarf in a state of purity (ie. with wudhu), then it is permissible for her to wipe over her headscarf when making wudhu after that. This is the correct position in the Hanbali school. This is the case whether it is possible for her to take her headscarf off or not.
So, for example, if she knows that she will have difficulty taking her headscarf off when she leaves the home, she should make wudhu, and she is then permitted to wipe over her headscarf if she needs to make wudhu again later.
The evidence for this is that the word ‘Khimar’ (scarf) is used in some narrations that state permissibility as reported in the Musnad of Imam Ahmad.
Secondly, wiping over the turban is authentically established for men in the Sunnah, so the headscarf is given the same ruling because women are more worthy of being allowed to wipe over the scarf due to the hardship of taking it off.
Thirdly, it is reported that some female companions used to wipe over their headscarves as reported from Um Salamah (r) who was one of the scholars of the companions.
As for the time frame then it is the same as wiping over footwear; a day and night for the resident, and three days and nights for the traveller.
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