Is brokerage money lawful or unlawful if a small amount of unlawful balance remains and is mixed with lawful money, knowing that he does not remember how much of the unlawful balance remained?

The thief must repent and return the stolen item to its owner. As for his work in brokerage, if it adheres to the Sharia (definition) regulations, then its profits are permissible and are not affected by charging his phone with stolen money. Indeed, the unlawful does not affect the permissibility of money earned through lawful work.