Is it permissible to take a sum of money in exchange for helping to obtain a residency permit for a foreign worker sponsored by another entity, knowing that the assistance is lawful and involves no harm?

If your benefit to the worker is limited to intercession (شفاعة) or sponsorship (كفالة), then it is not permissible to take a fee for it. This is because sponsorship is a contract of benevolence (عقود الإرفاق), and the Messenger of Allah, peace be upon him, said: "Whoever intercedes for his brother with an intercession, and he is given a gift for it, and he accepts it, then he has approached a great door from the doors of usury."

However, if the effort requires exertion, travel, or expense to extract documents, then it is permissible to take a reasonable wage (أجرة المثل) without excess. One should seek the immense reward from Allah for this work, as it is among the deeds most beloved to Him, in affirmation of the Almighty's saying: "Whoever intercedes with a good intercession will have a share from it," and the saying of the Messenger of Allah, peace be upon him: "The most beloved people to Allah are those most beneficial to people."