Is the hiring of an employee from another company, taking into consideration his high salary and the company's need for him, considered to be a "sale over the sale of one's brother," which is forbidden in Islamic law?

An employee must inform their employer before leaving, if that is stipulated in the contract, in accordance with the Almighty's saying: "O you who have believed, fulfill [all] contracts," and the hadith: "Muslims are bound by their conditions." This is especially emphasized if their departure without prior notification would cause harm to the employer.

There is no harm in accepting an employee's offer to work for you at a higher salary while they are still employed. This does not fall under the category of selling over a brother's sale, especially if their agreement with their current company does not prohibit their transfer, provided they notify them.

However, if you are the one who offered them to leave their work, then this is forbidden, like selling over a Muslim's sale. This includes renting over a brother's rental, or seeking to take someone else's place in a position of authority or a job.