Is the student considered sinful if he accepts his professor's help in succeeding in obtaining a Ph.D., given the suspicion that the professor overstepped boundaries to ensure his success, and is the money earned from working with this degree unlawful?

Doubt has no place here, and one should not pay attention to it, because the teacher is entrusted with his work, and the original presumption is the acquittal of his and the questioner's liability. Thus, whoever claims otherwise must provide proof. The rule agreed upon by scholars is that if a matter oscillates between being obligatory and not obligatory, then it is not obligatory, because the original presumption is the acquittal of liability until the obligation is definitively established.