In this paper, we investigate a communication system comprised of an energy harvesting (EH) source which harvests radio frequency (RF) energy from an out-of-band full-duplex relay node and exploits this energy to transmit data to a destination node via the relay node. We assume two scenarios for the battery of the EH source. In the first scenario, we assume that the EH source is not equipped with a battery and thereby cannot store energy. As a result, the RF energy harvested during one symbol interval can only be used in the following symbol interval. In the second scenario, we assume that the EH source is equipped with a battery having unlimited storage capacity in which it can store the harvested RF energy. As a result, the RF energy harvested during one symbol interval can be used in any of the following symbol intervals. For both system models, we derive the channel capacity subject to an average power constraint at the relay and an additional energy transmission cost at the EH source. We compare the derived capacities to the achievable rates of several benchmark schemes. Our results show that using the optimal input distributions at both the EH source and the relay is essential for high performance. Moreover, we demonstrate that neglecting the energy transmission cost at the source can result in a severe overestimation of the achievable performance.