Is what the husband's mother paid of Zakat al-Fitr on his behalf and on behalf of his family sufficient for the past five years, knowing that he did not give her the money, or is he required to make up for those years?

Zakat al-Fitr is obligatory upon a Muslim for themselves and for those whose maintenance is incumbent upon them, provided they possess what exceeds their needs and the needs of their dependents on the day and night of Eid. Otherwise, nothing is due from them. It is incumbent upon the husband to pay it on behalf of his wife, according to the preponderant opinion of scholars. If the husband is unable to pay it at the time it becomes obligatory, then the preponderant opinion is that it becomes obligatory upon the wife. If the husband voluntarily pays it on her behalf with her knowledge, the obligation is lifted from her. It is permissible to pay it in the original country, but it is preferable to pay it in the current place of residence.