Am I culpable for the period of time someone used electronic cigarettes that they purchased in my name, and what should I do about it?

Among the reasons for the removal of sin are error and forgetfulness, due to the Almighty's saying: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts intended," and the Almighty's saying: "Our Lord, do not impose blame upon us if we have forgotten or erred," and the saying of the Prophet, peace and blessings be upon him: "Indeed, Allah has overlooked for my Ummah [nation] error, forgetfulness, and what they are compelled to do." Therefore, there is no sin in assisting a person who has forgotten the حرمة (sacredness/prohibition) of what they intend to buy, while being keen to advise them.