If the period begins before sunset, even if it is a moment before, the woman’s fast is invalidated and she has to make up that day.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said in Majaalis Shahr Ramadaan, p. 39:
If the period begins whilst she is fasting, even if that is a moment before sunset, her fast is invalidated and she must make it up.
It is not permissible for her to fast when she is menstruating; if she does that, her fast is not valid.
Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (4/397):
If a menstruating woman intends to fast and refrains from eating and drinking even though she is aware that this is haraam, she is sinning and that will not avail her anything.
And Allaah knows best.