Is it permissible to accept a job offer from someone who acquired a large portion of his wealth through illicit means (archaeological excavation and selling of artifacts), and is the money earned from this partnership lawful? And is the income from supervising this person's projects lawful?

Excavating for antiquities and earning a living from them is not absolutely forbidden. If the antiquities are permissible to acquire and own, then trading in them is allowed. If a person earns a living from something that is not permissible, then dealing with him falls under the category of dealing with someone whose wealth is mixed with both lawful and unlawful, which is permissible. The described scenario falls under mudarabah, which is handing over money to someone to trade with it for a shared percentage of the profit. It is stipulated that the capital should not be guaranteed to the agent (amil), and that the share of both the capital owner and the agent be a shared percentage of the profit. However, if the capital owner asks the inquirer to supervise a project or provide a service without handing over capital, this is considered ijarah (leasing/hiring), and it is stipulated that the project must be permissible, and the wages and work must be specified.