Is it permissible for someone to fast on behalf of their deceased friend for missed days of fasting, even if they do not know the exact number of these days?

Scholars have differed on the ruling concerning a guardian fasting on behalf of a deceased person. If the deceased was able to make up the fasts before their death but did not do so, then it is recommended for their guardian to fast on their behalf. The guardian is understood as any close relative. As for a non-relative fasting on behalf of the deceased, it is permissible with the deceased's permission before their death, or with the guardian's permission. Otherwise, jurists have differed on its validity. If a non-relative fasts on their behalf with the guardian's permission, it is valid; otherwise, according to the more authoritative opinion, it is not. If the deceased's illness was continuous until their death, and they were unable to make up the fasts, then no one should fast on their behalf. In cases where fasting is valid, one should fast for the number of days owed by the deceased. If the number is unknown, one should fast for what is likely sufficient to clear the deceased's obligation.