Is it permissible for me to recover the cost of the recruitment visa, which I paid to my sponsor and which he did not return to me, by working partially in his establishment or by taking money from his proceeds?

If the visa applicant incurred expenses or faced hardship and travel, he is entitled to take what he spent along with a fair wage, with the visa sponsor's approval. The stipulated contract is not to be altered due to work or family circumstances, for adherence to agreed-upon conditions is obligatory, in fulfillment of Allah's saying: "O you who have believed, fulfill [all] contracts," and the Prophet's saying (peace be upon him): "Muslims are bound by their conditions." If what the sponsor took for the visa was the amount he spent plus a fair wage, and with your approval, then you have no right to claim anything back. However, if he took more, then you only have the right to claim back the excess amount.