Is money earned by an individual acting as an intermediary to complete a government transaction in exchange for a fee, which is then shared with another party who completed the transaction by utilizing their connections, permissible or impermissible (halal or haram)?

If what is paid is for effort, work, and time expended, then there is no harm in it, because agency (wakalah (definition)) is permissible for a fee. However, if it is merely mediation and intercession, then it is not permissible, due to the Prophet's (peace be upon him) saying: "Whoever intercedes for his brother with an intercession, and he (the brother) gives him a gift and he accepts it, then he has approached a great door from the doors of usury (riba)."