What is the ruling on the monthly salary received by the wife from an integration program, whose duties are performed by her father on her behalf without the knowledge of the entity providing the salary?

This action is not permissible because it is a circumvention of the system, a violation of the state's employment conditions, and an evasion thereof. The money earned from it is unlawful, due to the Prophet's (peace be upon him) saying: "Muslims are bound by their conditions, except for a condition that forbids what is lawful or permits what is unlawful."