Is it permissible for someone who intentionally broke their fast for a number of days in Ramadan during their youth, and was unable to make them up in their old age, to appoint someone to fast on their behalf for financial compensation? And have scholars differed on this issue?

Whoever intentionally breaks their fast in Ramadan (definition) without a valid legal excuse has committed a major sin and must repent. If one is unable to fast due to old age, they are not required to make up the fast, but rather must feed a poor person for each day they missed, and also feed another poor person for each day as expiation for delaying the make-up fast. As for one who neglects fasting in Ramadan while being obligated to do so, they must make up all the missed days, along with feeding a poor person for each day if they are able; but if they are poor, then making up the fast and repenting is sufficient for them. As for one who misses fasting due to a valid excuse, such as illness or travel, they must make up the fast.