Must the children fast an expiation for accidental killing (fasting for two consecutive months) on behalf of their deceased father, who did not fast it due to his ignorance of the ruling, and is continuity a condition in their fasting?

If someone kills a believer by mistake, expiation (kaffarah) and blood money (diyah) are obligatory. The expiation is either freeing a slave or fasting for two consecutive months. If the killer dies before performing the expiation, a slave should be freed from his wealth; if none is available, it is recommended for one of the heirs to fast two consecutive months on his behalf. It is not permissible to divide the fasting among the heirs because it contradicts the requirement of consecutive fasting. As for the blood money, it is obligatory upon the killer's 'Aqilah (male relatives on the father's side); if he has no 'Aqilah, then it is taken from his own wealth. It is given to the heirs of the deceased; if there are no heirs, then it goes to the public treasury (Bayt al-Mal).