Mobile battery energy storage systems (MBESs), also called power-to-mobility, have been field-validated as backup generation resources. However, the role of multi-energy coordination towards resilient distribution systems (DSs) against large area disasters is still not yet involved. To cope with such challenges, this paper proposes a computing optimal resilient operation model for post-disaster microgrid-penetrated DS recovery based on the energy-to-mobility approach. In this model, mobile multi-energy storages (MMESs) are invested and routed based on their different transportation mobility, while DS with consumer-side biogas-solar-wind multi-energy microgrids are topologized by network reconfiguration. The coordinated resilient operation of different recovery actions of DS, MMESs, and consumer-side microgrids is a difficult optimization problem as results of its inherent nonconvexities, temporal-spatial mobility and strong multi-energy couplings. The original mixed-integer non-linear programming (MINLP) problem is thus equivalently linearized and reformulated into a mixed-integer linear programming (MILP) for computation performance improvement. The proposed methodology is benchmarked and performed on a modified radial DS with three consumer-side microgrids. Numerical studies demonstrate the effectiveness and superiority of the energy-to-mobility scheme over MBESs on system resilient level and economy.