My personal opinion is that company A as the owner of the aircraft and employer of the pilot is conducting a charter operation to company B and in which case requires an AOC.
UNLESS it is a conglomerate of companies, for example Company A is the owner and operator of the aircraft and company A owns a controlling interest 51% in those companies for which it operates, company B, C, D making it a private operation wholly within that company group. The pilot must be employed by company A and hold at least a commercial licence. It comes down to who has operational control where the pilot is not the owner of the aircraft,