The Official Website of Grand Ayatollah Makarem Shirazi

if one has a doubt whether or not they have a qada fast due, they can observe recommended fast. But if they are certain that a qada fast is due on them, they cannot observe recommended fast. But they can make a vow to observe the recommended fast and observe fasting in term of the vow on the condition that they have time to perform the qada fast. So, if they for example owe 10 qada fasts, they should have at least 10 days by the time Ramadan arrives so that they can make up for the fasts. Furthermore, if one owes qada fasts, they can observe hired fasts on behalf of someone else. However, there are times where the number of qada fasts increases to such an extent that the exact number is forgotten, in which case the minimum number would be sufficient unless forgetting the number is due to negligence, meaning, one knew the number of lapsed fasts but they have forgotten out of negligence how many qada fasts they must keep, in which case the obligatory precaution demands that one should consider the maximum number of lapsed fasts they think are due on them. If one has qada fasts left over from a number of previous Ramadan and there is time for performing the qada, a fast of the last Ramadan, one can make up for the fasts of each of the Ramadan months. But if time is short, it is necessary that one performs the qada fast for the last Ramadan first. If one dies while the qada of prayer or fast is due on them, their eldest son has the obligation to keep the qada of their lapsed fasts and prayers. However, if the eldest son is not certain whether his parents have qada fast due on them, he is not obligated to keep the qada of fast for them. But if he knows that they have a few qada fasts due, he should make up for the fast as much as he is certain. Nevertheless, in circumstances in which one has failed to observe the fast of Ramadan due to a legitimate excuse such as menstruation, and has not managed to make up for the lapsed fast until the beginning of the Ramadan of the following year because of death, the eldest son is not required to make up for these fasts.