Is it permissible for me to act as an intermediary for companies with a friend who works in the tax authority, so that he can help them with the tax amount, and I take a commission from them without my friend taking a commission?

What your friend is doing by not taking bribes from clients is correct, because what an employee takes in exchange for his obligatory work is considered a forbidden bribe.

Regarding mediation in taxes: 1. Legitimate taxes: It is permissible to mediate in them and take a fee for the effort expended in completing transactions. 2. Forbidden taxes: It is not permissible to work in them except for one who intends to repel injustice or alleviate it from people, and knows that if he leaves the position, someone who will not do so or will increase in injustice will take it over. It is permissible for your friend to take a fee for his effort if he intends to achieve justice and reduce these taxes as much as he can. If he cannot achieve that, then it is not permissible for him to take a fee, and the matter reverts to the original prohibition. Assuming permissibility, it is not permissible for his friend to show favoritism by expediting transactions or reducing the tax merely because of his mediation.