Unmanned Aerial Vehicles (UAVs) in networked environments face significant challenges due to energy constraints and limited battery life, which necessitate periodic replacements to maintain continuous operation. Efficiently managing the handover of data flows during these replacements is crucial to avoid disruptions in communication and to optimize energy consumption. This paper addresses the complex issue of energy-efficient UAV replacement in software-defined UAV network. We introduce a novel approach based on establishing a strict total ordering relation for UAVs and data flows, allowing us to formulate the problem as an integer linear program. By utilizing the Gurobi solver, we obtain optimal handover schedules for the tested problem instances. Additionally, we propose a heuristic algorithm that significantly reduces computational complexity while maintaining near-optimal performance. Through comprehensive simulations, we demonstrate that our heuristic offers practical and scalable solution, ensuring energy-efficient UAV replacement while minimizing network disruptions. Our results suggest that the proposed approach can enhance UAV battery life and improve overall network reliability in real-world applications.