Energy sharing through a microgrid (MG) is essential for islanded communities to maximise the use of distributed energy resources (DERs) and battery energy storage systems (BESSs). Proper energy management and control strategies of such MGs can offer revenue to prosumers (active consumers with DERs) by routing excess energy to their neighbours and maintaining grid constraints at the same time. This paper proposes an advanced power-routing framework for a solar-photovoltaic (PV)-based islanded MG with a central storage system (CSS). An optimisation-based economic operation for the MG is developed that determines the power routing and energy sharing in the MG in the day-ahead stage. A modified droop controller-based real-time control strategy has been established that maintains the voltage constraints of the MG. The proposed power-routing framework is verified via a case study for a typical islanded MG. The outcome of the optimal economic operation and a controller verification of the proposed framework are presented to demonstrate the effectiveness of the proposed power-routing framework. Results reveal that the proposed framework performs a stable control operation and provides a profit of 57 AU$/day at optimal conditions.