Is it permissible to pay a salary to the son of a private school owner, who works elsewhere, without showing him on the payroll to avoid the state's legal requirements for his daily presence, and is the school owner free to dispose of his money and school, or does the state have the right to intervene?

It is not permissible to dispose of the funds of schools in which the state has a share in their capital except with its permission. However, if the state only supervises them and does not have a share, then the permission of the owner of the institution is what matters, and the state has no right to interfere, due to the saying of the Prophet, peace and blessings be upon him: "The property of a person is not lawful [to take] except with his willing consent."