Is the father obliged to pay Zakat al-Fitr on behalf of his adult son who intentionally broke his fast during Ramadan?

Neglecting the Ramadan fast is a grave sin, and its perpetrator is considered worse than an adulterer or an alcoholic, with their very Islam being called into question. It is obligatory for whoever abandons fasting to perform sincere repentance and to make up the days they intentionally missed. Zakat al-Fitr is obligatory for every Muslim, including those who intentionally break their fast in Ramadan, as it is an independent obligation. If the young man is an adult and capable of earning, his father is not obliged to spend on him or pay Zakat al-Fitr on his behalf. However, if he is incapable, his maintenance and Zakat al-Fitr become obligatory upon his father.