It is narrated from Muawiyah ibn Ammar, from Abu Abdullah عليه السلام, that he said: "If you wish to perform Tawaf on behalf of one of your brothers, go to the Black Stone and say, 'In the name of Allah سبحانه وتعالى, O Allah سبحانه وتعالى, accept this on behalf of [the name of the person].'"