Is it permissible to pay a commission or bonus to an employee in another company in exchange for increasing his company's purchases, or for him to obtain his management's approval for the purchase, and is this considered a bribe?

It is not permissible to pay a commission to an employee tasked with purchasing for your company, as this is considered bribery and forbidden gifts to employees. The Prophet (peace be upon him) informed that it is an act of embezzlement (ghulul). The employee receives his wage from his employer for the work of purchasing and seeking the best and cheapest options. Therefore, it is not permissible to give him anything extra for his work, unless the employer permits it and it does not involve deception or fraud.