She has to offer expiation for having intercourse during the day in Ramadan with her previous husband, and it is very difficult for her to tell her current husband. Can she offer expiation by feeding poor persons without his knowledge?

Firstly:

The woman who had intercourse during the day in Ramadan must offer expiation, if she was aware of the ruling, remembered that it was Ramadan and did that willingly, according to the majority of fuqaha’, except the Shaafa‘is.

See also the answer to question no. 106532.

Secondly:

According to the view that it is obligatory to offer expiation, the options come in a certain order, according to the majority. She must manumit a slave; if that is not possible, then she must fast for two consecutive months; if she is not able to do that, then she must feed sixty poor persons.

Maalik – and Ahmad, according to one report – are of the view that the person has a choice with regard to how expiation is offered, because of the report narrated by Ahmad (7692), Maalik in al-Muwatta’ (28), Muslim (111) – by whom this version was narrated – and Abu Dawood (2392) from Abu Hurayrah, that the Prophet (blessings and peace of Allah be upon him) instructed the man who broke the fast in Ramadan to manumit a slave, or fast for two months, or feed sixty poor persons.

According to a version narrated in al-Muwatta’ and by the others, from Abu Hurayrah: A man broke the fast in Ramadan, so the Messenger of Allah (blessings and peace of Allah be upon him) instructed him to offer expiation by manumitting a slave, or by fasting for two consecutive months, or by feeding sixty poor persons. The man said: I cannot afford to do that. Then a basket of dates was brought to the Messenger of Allah (blessings and peace of Allah be upon him), so he said: “Take this and give it in charity.” He said: O Messenger of Allah, there is no one in greater need than me. The Messenger of Allah (blessings and peace of Allah be upon him) smiled so broadly that his eyeteeth could be seen, then he said: “(Take it and) eat it.”

Ibn ‘Abd al-Barr (may Allah have mercy on him) said in al-Istidhkaar (3/311): According to ash-Sha‘bi and az-Zuhri, the view of Maalik, that the individual in this situation  has the choice [between these three options], is supported by this hadith, which is the evidence quoted by Maalik. However, Maalik preferred the option of feeding the poor because it is more appropriate as compensation for not fasting. Do you not see that in the case of pregnant and nursing women, one who is elderly and one who neglected to make up missed fasts before the next Ramadan came, none of them were instructed to manumit a slave or to fast for two months in addition to making up the missed fasts; rather they were instructed to feed the poor. That is because feeding the poor is appropriate in the case of fasting, and this is in accordance with the basic principles of Islam.

This is the view that was favoured by Maalik and his companions.

Ibn Wahb said, narrating from Maalik: Feeding the poor is dearer to me in that case than manumitting a slave and so on.

Ibn al-Qaasim said, narrating from Maalik: He did not know anything except feeding the poor; he did not choose the option of manumitting a slave or fasting  two months.

There is a report from ‘Aa’ishah about the one who had intercourse with his wife in Ramadan, and in that report there is no mention of feeding the poor.

Ash-Shaafa‘i, ath-Thawri and all the Kufis were of the view that the expiation of one who broke the fast in Ramadan by having intercourse deliberately is the same as the expiation for one who divorced his wife by zihaar [a jaahili form of divorce in which a man says to his wife: “You are to me as my mother’s back”], and the options should be taken in order. End quote.

The evidence given by the majority is the fact that most reports of this hadith mention the options for expiation in a particular order.

Ibn Hajar said: Some of the scholars – such as al-Muhallab and al-Qurtubi – reconcile between the two reports by understanding them as referring to different stories, but this is far-fetched, because it is one story and the source is the same, and the basic principle is that there are not many stories.

Some of the scholars interpreted it as being an order of priority, and stated that it is permissible to choose one of the options.

End quote from Fath al-Baari (4/168).

We have previously discussed this issue in several answers, and stated that the correct view concerning it is the view of the majority.

Please see the answers to questions no. 189853, 131660 and 106535.

But the view of Imam Maalik concerning this issue is a strong view, for which there is evidence, as we have noted above. It is a valid view and is not to be ignored; how can it be ignored when it is the view of Imam Maalik, and we know what a great scholar he is. 

Based on that: If following the view of the majority and fasting will result in obvious harm for this woman, then there is nothing wrong with her following the view of Maalik and feeding sixty poor persons with her own money, without her husband knowing.

And Allah knows best.