Women covering their hair upon hearing the athan (call for prayers) has no basis in Islam. Doing so religiously is a reprehensible innovation (bid’ah). On the contrary, a woman should hear the athan and repeat what th meuezzin says in whatever condition she is, whether her head and body are properly covered in hijab or not. The ruling is similar when she hears recitation of the Qur’an: she does not have to observe the hijab.
Allah knows best.
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