Electrochemical energy storage (ES) units (e.g. batteries) have been field-validated as an efficient back-up resource that enhance resilience of the distribution system in case of natural disasters. However, using these units for resilience is not sufficient to economically justify their installation and, therefore, these units are often installed in locations where they incur the greatest economic value during normal operations. Motivated by the recent progress in transportable ES technologies, i.e. ES units can be moved using public transportation routes, this paper proposes to use this spatial flexibility to bridge the gap between the economically optimal locations during normal operations and disaster-specific locations where extra back-up capacity is necessary. We propose a two-stage optimization model that optimizes investments in mobile ES units in the first stage and can re-route the installed mobile ES units in the second stage to avoid the expected load shedding caused by disaster forecasts. Since the proposed model cannot be solved efficiently with off-the-shelf solvers, even for relatively small instances, we apply a progressive hedging algorithm. The proposed model and progressive hedging algorithm are tested through two illustrative examples on a 15-bus radial distribution test system.