This paper investigates simultaneous wireless information and power transfer (SWIPT) for a decode-and-forward (DF) full-duplex relay (FDR) network. A battery group consisting of two batteries is applied to utilize the relay-harvested energy for FDR transmission. The virtual harvest-use model and harvestuse-store model are considered, respectively. By switching between two batteries for charging and discharging with the aid of power splitting (PS), concurrent source and relay transmissions can overcome spectral efficiency loss compared to half-duplex relay (HDR)-assisted PS-SWIPT. The outage probability for the virtual harvest-use model is presented in an exact integral-form and the optimal PS (OPS) ratio that maximizes the end-to-end signal-to-interference-plus-noise ratio (e-SINR) is characterized in closed-form via the cubic formula. The fundamental tradeoff between the e-SINR and recycled self-power is quantified. The OPS ratios and corresponding outage probabilities in noiselimited and interference-limited environments are also derived. In the harvest-use-store model, a greedy switching (GS) policy is implemented with energy accumulation across transmission blocks. The OPS ratio of the GS policy is presented and the corresponding outage probability is derived by modeling the relays energy levels as a Markov chain with a two-stage state transition. Numerical results verify the performance improvement of the proposed scheme over HDR-assisted PS-SWIPT in terms of outage probability and average throughput.