Is it permissible to accept money from a brother who works in the tobacco trade and is said to deal in lotteries, with his knowledge that the money is mixed, coming from both a lawful and an unlawful source?

If your brother has lawful money other than what he earns from prohibited matters, there is no harm in accepting his gift. However, if he possesses only unlawful money, it is not permissible to accept a gift purchased directly with his money, unless he purchases it on credit, in which case there is no harm. He should be advised to abandon selling tobacco and participating in gambling, based on the Almighty's saying: "O you who have believed, indeed, intoxicants, gambling, [sacrificing on] stone altars [to other than Allah], and divining arrows are but defilement from the work of Satan, so avoid it that you may be successful." And tobacco is forbidden to sell and consume, based on the hadith: "Indeed, when Allah Almighty prohibits the eating of something, He also prohibits its price."