Is the fast of one who intended to fast in her heart before Fajr and drank a glass of water valid, even though she did not say, "Today I will fast Ramadan"?

If a woman becomes pure after Fajr, her fast is invalid, and she must make it up. However, if she becomes pure before Fajr and the intention to fast is made contingent upon purity, then if she has a regular habit by which she knows the cessation of blood before Fajr, her fast is valid, and she is not required to make it up. But if she does not have a regular habit, then the jurists have stipulated the obligation of making up the fast due to the lack of certainty in the intention. Meanwhile, Al-Nawawi holds that the fast is valid if she is a beginner or accustomed to her habit concluding at night. And based on the choice of Sheikh Al-Islam Ibn Taymiyyah, the fast is valid even with hesitation in the intention if it is based on what can be known with certainty.