This paper studies a novel user cooperation method in a wireless powered cooperative communication network (WPCN) in which a pair of distributed terminal users first harvest wireless energy broadcasted by one energy node (EN) and then use the harvested energy to transmit information to a destination node (DN). In particular, the two cooperating users exchange their independent information with each other so as to form a virtual antenna array and transmit jointly to the DN. By allowing the users to share their harvested energy to transmit each other's information, the proposed method can effectively mitigate the inherent user unfairness problem in WPCN, where one user may suffer from very low data rate due to poor energy harvesting performance and high data transmission consumptions. Depending on the availability of channel state information at the transmitters, we consider the two users cooperating using either coherent or non-coherent data transmissions. In both cases, we derive the maximum common throughput achieved by the cooperation schemes through optimizing the time allocation on wireless energy transfer, user message exchange, and joint information transmissions in a fixed-length time slot. We also perform numerical analysis to study the impact of channel conditions on the system performance. By comparing with some existing benchmark schemes, our results demonstrate the effectiveness of the proposed user cooperation in a WPCN under different application scenarios.