She became pure after Zuhr; does she have to fast for the rest of the day?

Praise be to Allah.

Firstly: 

It is not permissible for women who are menstruating or bleeding following childbirth to fast during their menses or nifaas, according to scholarly consensus. 

It says in al-Mawsoo’ah al-Fiqhiyyah (18/318): 

The fuqaha’ are unanimously agreed that it is haraam for menstruating women to fast in all cases, whether the fast is obligatory or naafil, and it is not valid if she does it, because the Prophet (peace and blessings of Allaah be upon him) said, according to the hadeeth of Abu Sa’eed: “Is it not the case that when she menstruates she does not pray or fast?” They said: Yes. He said: “That is her shortcoming in religious commitment.” So if a woman sees the blood at any time of the day, her fast becomes invalid. Ibn Jareer, al-Nawawi and others narrated that there was consensus on this point. … The fuqaha’ are also unanimously agreed that she has to make up missed obligatory Ramadaan fasts, because ‘Aa’ishah (may Allaah be pleased with her) said concerning menstruation: “That used to happen to us, and we were enjoined to make up the fasts but we were not enjoined to make up the prayers.” Al-Tirmidhi, Ibn al-Mundhir, Ibn Jareer and others narrated that there was consensus on this point. End quote. 

Thus it is clear that it is not valid to fast the day on which a woman becomes pure from menses, and she has to make up this day after Ramadaan. 

But then the scholars differed as to whether she has to refrain from eating and drinking for the rest of that day out of respect for the sanctity of the blessed month, or not. There are two scholarly points of view, the more correct of which is the view of the Maalikis and Shaafa’is, which is that she does not have to refrain from eating and drinking. This is the view favoured by Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) in al-Sharh al-Mumti’ (6/344). 

It says in al-Mawsoo’ah al-Fiqhiyyah (18/318):  

There is no difference of opinion among the fuqaha’: if her menses ends after Fajr, then if she fasts on that day it does not count and she has to make it up. But in that case she should refrain from eating and drinking according to the Hanafis and Hanbalis, but according to the Maalikis it is permissible for her to eat, and it is not recommended for her to refrain from eating and drinking. According to the Shaafa’is she does not have to refrain from eating and drinking. End quote. 

And Allaah knows best.