What is the ruling on a brother working for a company that uses forged invoices to reduce taxes, knowing about it and participating in their recording? And must he leave this job? And what is the ruling on the money he saved from his salary in this company?

The type of taxes the manager forges invoices to evade must be determined. If the taxes are legitimate, then evading them and the accountant's assistance in doing so are forbidden. The accountant must refuse, even if it leads to his dismissal, unless he has no other means of livelihood. However, if the taxes are unjust and illegitimate, there is no sin in evading them or assisting the manager in doing so. Your brother's work as an accountant in the company is permissible, and the manager's request for him to do something forbidden does not affect the permissibility of the job or salary, as long as it is not part of the primary contract.