Must a breastfeeding woman who has started solid feeding for her child break her fast in Ramadan in order to be able to fast, and is she sinful if she fasts?

A breastfeeding woman is permitted to break her fast in Ramadan if she fears for herself or her child, and she must make up the missed days. If she fears only for her child, then she must make up the missed days and feed a poor person for each day. However, if fasting does not harm her or her child, or if there is an alternative to breastfeeding such as formula milk or another wet nurse whom the child accepts, then she must fast and is not permitted to break it.