Is it permissible to continue in a business partnership that sells cigarettes, without investing money in it or receiving its profits, due to the lack of any other means of livelihood?

You are not permitted to partner with this person if you find another means of livelihood, because he has openly committed a reprehensible act, and it is obligatory to denounce him by shunning him and refraining from partnering with him. However, if you do not find another means of earning a living, then there is no harm in partnering with him in the shop, provided that you do not participate in the capital of the cigarette trade or its profits, for necessities permit the prohibited.