Is what the partner did – taking a portion of his partner's capital to invest it with a guarantee of the principal – permissible or forbidden, and is he allowed to deduct from the profits in exchange for his supervision?

Two points should be noted: First: If your supervision of the company's work was voluntary and without seeking compensation, then you are not owed anything for it. However, if you intended a reward, then you have the right to demand fair compensation (ujrat al-mithl).

Second: The company's funds in your possession are a trust (wadi'ah), and you are not liable for them except in case of negligence. Your trading with your partner's share without his permission is disliked (makrooh). Any profit generated from it is yours, and you are liable for that trust during your encroachment upon it. You are entitled to fair compensation (ujrat al-mithl) for your efforts, unless you were acting voluntarily.