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

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.