We study the problem of joint information and energy transfer in a binary two-hop channel with an energy harvesting relay. We consider a finite battery size at the relay and energy loss in transmitting energy. In other words, to be able to send an energy-contained symbol, the relay must receive multiple energy-contained symbols. Thus, we face a kind of channel with memory. We model the energy saved in the battery as the channel state with the challenge that the receiver does not know the channel state. We propose two different achievable schemes, the first one is based on state-dependent superposition coding and the second one is based on the equivalent timing channel approach. Both of our schemes are based on block Markov coding and backward decoding techniques. Due to these two approaches, we find achievable rates with a single-letter expression for the model.