What is the ruling on working as an archaeological inspector, given that one does not visit some of the sites assigned for inspection, and disposes of a portion of the salary by spending it on charitable causes? Is the money earned from this job lawful?

You must adhere to the employment contract that mandates genuine inspection. Deducting part of the salary does not absolve you from abiding by the contract's terms. The direct supervisor's knowledge of the employee's negligence and their overlooking it does not permit dereliction of duty, unless the supervisor is authorized to do so and has the authority to grant permission. The salary received unlawfully must be returned to the responsible entity, even through indirect means. If restitution is impossible, it should be spent on public welfare. The fact that the entity will spend it on museums does not justify not returning it to them.