What is the ruling of Islamic law on taking a sum of money in exchange for sponsoring someone who comes to work, with his consent to the agreement and his freedom to choose his work?

This issue falls under the category of 'Thaman al-Jah' (price for status/influence), which refers to a person using their status or influence to help another obtain their right. Examples include a person of standing striving to remove injustice from someone who has been wronged. Scholars have differed on the permissibility of taking payment for such efforts, with some absolutely prohibiting it, others deeming it disliked (makrooh), and a detailed view permitting it if the person of status incurred expenses or exerted effort. This latter view is the most preponderant.

Accordingly, it is permissible for you to take from the sponsored individual an amount equivalent to the wage for someone like you, covering your effort and expenses for obtaining the necessary documents. However, it is not permissible to exceed this amount with the intention of profit.