Distribution networks have always been exposed to outages due to various internal and external causes. During emergencies, the damaged areas are disconnected and as a result, a portion of the connected loads remained unmet until ending required repairs. Accordingly, utilizing the total renewable potential in smaller islands may be unmanageable and result in curtailment. In this paper, a method is proposed to overcome these challenges by utilizing a fleet of mobile battery storage (MBS) systems. The MBSs will overcome renewable curtailment and unmet load simultaneously during emergencies via a shift in the produced energy. The excess energy produced in the islands with extra generation will be stored and then used at another location and time in the islands without production adequacy. To do this, a multi-stage and spatio-temporal operation model for a fleet of truck-mounted MBS systems based on road transport is proposed. Both time and cost of transportation are considered and modeled by linear formula. The battery lifetime and full four-quadrant power factor of the integrated inverter are also considered. The proposed model aids to decrease computational burden by decomposing the transportation model from the distribution network. Besides, it ensures the minimum cost operation while maximizing renewable resources utilization trapped on small islands. The model is linear and capable of handling real-life and large-scale systems when integrated into commercial distribution software. The model is validated by implementation on the 33-bus distribution grid coupled with a 15-node transportation network and results demonstrate increased resilience besides enhanced renewable resources utilization.