We consider a fading communication link where the transmitter is powered by the receiver through wireless energy transfer (WET). A typical application scenario for this is the transmitter being a simple sensor while the demand for data is created by an application running at the receiver side and pulled from the transmitter as needed. We formulate two offline transmission scheduling problems: the transmitter-centric WET transmission optimization problem, where the schedule is computed by the transmitter, and the receiver-centric WET transmission optimization problem, where the receiver computes the schedule. We provide explicit solutions of both problems and propose online policies that rely on using the estimated water level values for each case. Our formulation allows direct optimization of energy efficiency in contrast to other EH transmission scheduling formulations in the literature. We prove some equivalence results under the special case of fixed channels.