Is it permissible to sponsor an orphan with the father's money, given the son's sincere intention to sponsor, and is the son considered his sponsor so that he may attain the virtue of sponsoring an orphan?

Congratulations on engaging in the pursuit of Islamic knowledge, for it is among the most important and excellent matters that rectify one's faith and deeds, and benefit others. It is superior to all other works that serve society. As for sponsoring an orphan, its reward is immense. If you acquire wealth, whether it is a gift from your father or you obtained it through other means, Allah will grant you the reward mentioned in the hadiths if you fully sponsor an orphan, which includes caring for them, spending on their needs, educating them, and disciplining them. If they do not accept sponsorship in your name, your father can pay the money without disclosing that you are the sponsor, or you can find an orphan among your relatives, neighbors, or others.