Is it permissible for the children of a deceased woman to perform expiation (kaffarah) for unintentional killing on her behalf (fasting 60 days), and how can they divide the fasting period among themselves?

Fasting on behalf of the deceased is a matter of scholarly disagreement, but the preponderant opinion is the permissibility for the guardian (wali) to fast on behalf of the deceased unconditionally, whether it is for the fast of Ramadan, a vow, or anything else, due to the authentic Ahadith which have no opposing evidence.

The more cautious approach is for one of the children to fast on behalf of their mother for the expiation of Dhihar (declaratory divorce) if freeing a slave is not possible, provided that the one fasting is a single person, due to the necessity of continuous fasting. Indeed, continuous fasting cannot be distributed among the heirs; so either one of them fasts, or they feed a poor person for each day.