Is it permissible to report a manager to her superiors for her improper practices, such as exploiting employees for personal work during official hours, with the intention of seeking revenge and exposing her administrative corruption?

If you feel that you have been wronged by the manager who deducted from your salary without just cause, you can escalate the matter to higher authorities to seek justice; this is the correct way to handle such a situation. Her exploiting her authority in a way that is not permissible by Sharia is forbidden. Informing the authorities is a duty because it falls under the category of giving advice, as the Prophet (peace be upon him) said: "Religion is advice." However, the reporting must be done with the intention of drawing closer to Allah and fulfilling the duty of responsibility, not out of revenge.