What is the ruling on the financial sums taken by two parties in exchange for appointing a job seeker to a company, half of which is owned by one of the parties, and are such transactions permissible in Islam?

It is permissible for a job seeker to pay a sum of money to someone who guides him or provides him with a job opportunity. This falls under the category of a ju'alah (fee/commission), which is permissible in exchange for a lawful service.

As for the person who takes the money: if he is responsible for employment, it is not permissible for him to take the money, because it is a bribe, not a ju'alah. Just as returning a found item (luqtah) is a religious obligation, so too is employing those who are deserving. If he is not responsible for employment, then he may take the ju'alah and share it with the other party.

A condition for the permissibility of this act is that it must not involve employing an undeserving person at the expense of a deserving one, for that is a betrayal of Allah, His Messenger, and the believers.