Can a woman be an executor under Islamic law?

They are conditions of validity. The wasi must be of age and of sound mind, Muslim, and of established integrity (‘adala — in the Maliki formulation, trustworthiness and the competent handling of a child’s property). An appointment that fails one of these does not take effect at all: a Muslim cannot validly appoint a non-Muslim over his children or his estate, and Ibn Qudama records Malik and al-Shafi’i, with one of the two reports from Ahmad, as holding the same of a person of doubtful integrity. The Shafi’i list adds that the wasi be free, not an enemy of the person in his charge, and not of unknown character; a blind man may serve. The Maliki school adds that a wasi who later loses a qualification — who apostatises, or becomes incapable — is removed.

Sources: al-Fiqh ‘ala al-Madhahib al-Arba‘a, vol. 3, “Mabhath al-wasi al-mukhtar” (the chosen executor), school by school (‘Abd al-Rahman al-Jaziri (d. 1360 AH)) · al-Mughni, Kitab al-Wasaya, fasl 4773: “fi man tasihhu’l-wasiyyatu ilayhi wa man la tasihh” (who may be appointed wasi) (Ibn Qudama al-Maqdisi (d. 620 AH)) — each school’s list of conditions set out separately in al-Jaziri, and Malik, al-Shafi’i and Ahmad separately named in al-Mughni on the person of doubtful integrity.

The appointment stands; the judge fixes it. Where the person named is a minor, a non-Muslim, or of doubtful integrity, the appointment is valid and anything he does before he is removed takes effect — but the judge must replace him with someone qualified, substituting a Muslim for a non-Muslim, and removing a person of doubtful integrity only where he is actually suspected with the money. A wasi who meets every condition may not be removed by the judge at all, because he stands in the place of the deceased who chose him. Ibn Qudama states that a Muslim’s appointment of a non-Muslim is invalid with no disagreement he knows of; al-Jaziri records this Hanafi rule expressly, so the attribution of unanimity is not one we can pass on.

Sources: al-Fiqh ‘ala al-Madhahib al-Arba‘a, vol. 3, “Mabhath al-wasi al-mukhtar” (the chosen executor), school by school (‘Abd al-Rahman al-Jaziri (d. 1360 AH)) · al-Mughni, Kitab al-Wasaya, fasl 4773: “fi man tasihhu’l-wasiyyatu ilayhi wa man la tasihh” (who may be appointed wasi) (Ibn Qudama al-Maqdisi (d. 620 AH)) — the Hanafi conditions, and the valid-but-removable structure, set out in al-Jaziri; Abu Hanifa separately named in al-Mughni on the person of doubtful integrity.