Is it permissible for me to use the internet from a device my brother bought with ill-gotten money, knowing that I will pay the monthly subscription with lawful money?

What your brother took from illicit money pertains to his responsibility, not to the specific item he purchased. The device is his property, and there is no harm in you using it. Your brother must clear himself of the illicit money by returning it to its rightful owners if they are identifiable, or by spending it on the welfare of Muslims and the poor if they are not identifiable. You must advise him to repent.