When is the father entitled to regain custody of his son from his ex-wife after the judge ruled in favor of the mother for custody?

The preponderant opinion is that the custody period ends at the age of discernment (the seventh year). After that, the child is given a choice between their parents. If the child chooses one of them, they remain with that parent. If the child does not choose, lots are cast between them, unless there is an impediment in one of them, such as immorality. The mother's right to custody is forfeited if she marries. The father has the right to take the child unless there is someone more entitled to custody, or if there is someone more entitled and they waive their right. Disputes are resolved by referring to the Sharia court.