She has to meet the requirements outlined in the photo request. Good Luck.
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I agree with my colleagues. Her facial features should be visible, at a minimum. That is the purpose of the picture, i. e to identify one individual from another. Therefore, if her veil hides her individual facial features, it would not be sufficient for official purposes of immigration proceedings/applications. You could certainly find a place where a woman can take her picture in seclusion for modesty purposes, if her/your religion requires it. Good luck!
This advice does not form an attorney-client relationship and is merely informative. It should not by itself be relied upon to address a legal concern.