Is this income considered illicit and is the questioner responsible for it, and must he leave his job, in a case where the employer deducted a sum from a colleague, which resulted in the colleague leaving his job due to a mistake the colleague committed, knowing that the employer overlooks similar mistakes made by the questioner?

You must act in the best interest of the hotel owner and not take any action without his explicit or customary permission. If your legitimate action results in an employee's dismissal, then you bear no sin. Your colleague, who did not verify the account, is considered negligent in his work, and the hotel owner has the right to deduct the amount from him. You have the right to inform the hotel owner after advising your colleague first. If he does not respond and the matter becomes difficult, then you are obliged to inform the hotel owner. The dismissal of your colleague does not affect the lawfulness of your work and your new salary, unless you have wronged him.