Is it valid to pray Dhuhr on Friday immediately upon hearing the Dhuhr Adhan, or must it be after the completion of the Jumu'ah prayer in the mosque?

A woman's prayer at home is not tied to the completion of the Friday prayer at the mosque, as a woman is not obligated to perform the Friday prayer. The Adhan (definition) (call to prayer) at the time of the sun's decline (zawal) signals the entry of the Dhuhr prayer time for her. Therefore, she is permitted to pray upon hearing the Adhan without waiting for the completion of the Friday prayer, taking into account time differences and ensuring that the Dhuhr time has indeed entered in her locality.