Is it permissible to inform the management that a new employee is incompetent and should be replaced by a Muslim, especially since he lacks sufficient experience, takes time to learn, and resigned from his previous job after accepting this one?

If an agreement is made with an employee for a fixed-term job, it is obligatory for both parties to fulfill it, as a lease contract is binding and cannot be revoked except by mutual consent. The fact that the employee is non-Muslim does not permit breaching the contract with him, based on the words of the Almighty: (O you who have believed, fulfill [all] contracts) and His saying: (O you who have believed, do not betray Allah and the Messenger or betray your trusts while you know [the consequence]).

However, if the condition for his employment was the ability to learn quickly, and he was given a probationary period, then it became clear that he lacked this ability, the agreement may be terminated. But if the company agreed to employ him and he left his previous job, then it is obligated to fulfill its commitment to him until the end of his contract.