Can a woman whose fast is broken because of menstruation in Ramadaan eat?

When women who are menstruating or bleeding following childbirth become pure during the day in Ramadaan (i.e., the bleeding stops), and when a traveller arrives at his destination, and when a sick person who stopped fasting recovers, they do not gain anything by refraining from eating during the day. They broke their fast for a reason, and making them refrain from eating is a matter which requires a shar’i text as proof. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked:  

If a woman who is menstruating or bleeding following childbirth becomes pure during the day in Ramadaan (i.e., the bleeding stops), does she have to refrain from eating and drinking? 

He replied: 

If a woman who is menstruating or bleeding following childbirth becomes pure during the day in Ramadaan, she does not have to refrain from eating and drinking, and she may eat and drink, because refraining from doing so will not benefit her in any way, as she has to make up that day anyway. This is the view of Maalik and al-Shaafa’i, and is one of the two views narrated from Imam Ahmad. It was narrated that Ibn Mas’ood (may Allaah be pleased with him) said: “Whoever eats at the beginning of the day, let him eat at the end,” i.e., if it was permissible for him not to fast at the beginning of the day, it is permissible for him not to fast at the end of it. End quote. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen, 19/question no. 59 

As for the guidelines on that: 

Some of the scholars said that those who are permitted not to fast in Ramadaan, such as the sick, travellers and menstruating women, should not show that they are not fasting, lest they be accused of lacking in religious commitment by those who do not know that they are excused.  

Others are of the view that if the reason for the excuse is obvious, there is nothing wrong with them showing that they are not fasting, but if the reason is invisible, then they should break their fast in secret. The second view is more correct. 

Al-Mardaawi said in al-Insaaf (7/348): 

Al-Qaadi said: The one who eats openly in Ramadaan is to be denounced, even if there is an excuse. It says in al-Furoo’: It seems that it is not allowed in any case. It was said to Ibn ‘Aqeel: Should travellers, the sick and menstruating women be prevented from breaking their fast openly lest they be accused? He said: If the reason is invisible, they should not be allowed to break the fast openly, such as one who is sick with no outward signs of sickness and a traveller on whom there is no sign of travelling.” End quote. 

And Allaah knows best.