What is the ruling on a breastfeeding woman breaking her fast in Ramadan, and is it permissible for her to use formula milk to feed her child so that she can fast?

A nursing mother is permitted to break her fast and is only required to make up the missed days if she fears for herself or her child due to fasting, based on the Prophet's (peace be upon him) saying: "Indeed, Allah Almighty has relieved the traveler from fasting and half of the prayer, and the pregnant and nursing woman from fasting." If she does not fear, then she is not permitted to break her fast. There is no harm in feeding the child formula milk to enable the mother to fast, provided that the child is not harmed by it. In this case, the mother must fast.