Is a prayer considered valid if a woman performs it without wearing a headscarf outside of prayer times?

The hijab (definition) is an obligatory duty upon the Muslim woman. A Muslim woman's failure to wear the hijab outside of prayer is an act of disobedience to Allah. A Muslim woman must emulate the righteous women and the Mothers of the Believers. Her prayer is valid as long as she performs it with its conditions, pillars, and duties, and her not wearing the hijab outside of prayer does not invalidate her prayer. A Muslim woman must obey Allah the Almighty in all her states, and not only during prayer.