The performance of open quantum batteries (QBs) is severely limited by decoherence due to the interaction with the surrounding environment. So, protecting the charging processes against decoherence is of great importance for realizing QBs. In this work we address this issue by developing a charging process of a qubit-based open QB composed of a qubit-battery and a qubit-charger, where each qubit moves inside an independent cavity reservoir. Our results show that, in both the Markovian and non-Markovian dynamics, the charging characteristics, including the charging energy, efficiency and ergotropy, regularly increase with increasing the speed of charger and battery qubits. Interestingly, when the charger and battery move with higher velocities, the initial energy of the charger is completely transferred to the battery in the Markovian dynamics. In this situation, it is possible to extract the total stored energy as work for a long time. Our findings show that open moving-qubit systems are robust and reliable QBs, thus making them a promising candidate for experimental implementations.