AlSalaam Alikum Can a woman who's declared Shahadah but not praying who sends needed money to her poor family consider that money Zakat?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

The money which the woman whom you referred to in the question sent to her poor relatives without intending it as Zakat, is not considered as Zakat and it is not permissible for her to consider it as such because for Zakat to be accepted, when the person gives it, he should intend it as Zakat as clarified in Fatwa 85964. However, it is permissible for her to consider the money which she will send in the future as Zakat and intend it as Zakat, provided the people to whom she sends the money are among the people who are eligible for Zakat as mentioned in Fatwa 88368, and provided that she is not obliged to spend on them, like the parents for instance.

It should be noted that Zakat is not obligatory on money unless the money reaches the Nisaab (i.e. the minimum amount liable for Zakat) and a whole lunar year elapses since she possessed it, as clarified in Fatwa 85396.

However, what is more important than the above, is the issue of her not praying. The Prayer is the core of religion and the most important pillar of Islam after The Two Testimonies of Faith. Indeed, many scholars are of the view that a person who abandons the prayer is out of the fold of Islam as clarified in Fatwa 85264.

Therefore, it is an obligation to advise that woman and inform her that uttering The Two Testimonies of Faith necessitates performing the other pillars of Islam, the most important of which is the prayer. Then, if she persists on abandoning the prayer after knowing that performing it is an obligation, it is feared that she is a non-Muslim (a disbeliever), and hence, Zakat is not accepted from her. Allaah Says (what means): {And what prevents their expenditures from being accepted from them but that they have disbelieved in Allaah and in His Messenger.}[Quran 9:54]. 

For more benefit on giving Zakat to the relatives, please refer to Fataawa 87358 and 83559, and to Fatwa 82875 on the ruling of paying Zakat to non-Muslims.

Allaah Knows best.