Answered by Shaykh Faraz Rabbani
Question: If a woman doesn’t wear her hijab outside can her prayer be accepted in view of the hadith Allah does not accept the prayer of a woman who has reached puberty unless she wears a veil.
Answer: Walaikum assalam wa rahmatullahi wa barakatuh,
I pray this finds you in the best of health and spirits.
The hadith you mention refers to the condition of the validity of the prayer itself being that a woman cover in the prayer. While the hijab is a religious obligation–as is proper covering for both men and women in Islam–the acceptability of one’s other spiritual works isn’t dependent on wearing hijab.
Rather, one should do what one can without hesitation; ask Allah for increase in guidance and good; and commit in life to strive to be pleasing to Allah, in actions and conduct–and to embrace the beautiful way of the Beloved Messenger of Allah (peace & blessings be upon him & his folk) in all aspects of one’s life.
And Allah alone gives success.