To overcome finite lifetime bottleneck in the ubiquitous deployment of low-power wireless devices in Internet-of-Things, we propose a novel integrated information relay and energy supply (i2RES)-assisted RF harvesting co-operative communication model. i2RES aids the communication between two distant energy-constrained wireless nodes by: 1) RF energy transfer to the source and 2) relaying source data along with supplying energy to the destination. To enable efficient i2RES-powered information transfer to the destination, we first derive and then maximize the delay-limited achievable throughput over Rician channels by jointly optimizing time allocation for information and energy transfer along with relative position of i2RES between source and destination. Although the throughput maximization problem is nonconvex and highly nonlinear, we prove its generalized-convexity and obtain the global-optimal numerical solutions. To gain analytical insights, we also derive tight closed-form approximation for the optimized solutions. Numerical results validate the analysis and demonstrate significant gain in throughput performance via our proposed optimization schemes under practical hardware constraints. Finally, we discuss how the analysis and optimization results can be extended to general RF-EH system settings with relaxed constraints.