Structural characteristics on fluoride ion storage and conduction mechanism in La1.2Sr1.8Mn2O7, and its fluoridated materials, La1.2Sr1.8Mn2O7F and La1.2Sr1.8Mn2O7F2, for an all-solid-state fluoride ion battery positive electrode with a high volumetric capacity surpassing those of lithium-ion ones have been revealed using the Rietveld method and maximum entropy method. In La1.2Sr1.8Mn2O7, once the F- ions are taken into the NaCl slabs in its crystal through the charging process, it forms two stable fluoride compounds, La1.2Sr1.8Mn2O7F and La1.2Sr1.8Mn2O7F2, with the help of the Mn oxidation reaction. In these oxyfluorides, thermal vibrations of the F- ions inserted are much larger, especially in the a-b plane, than along the c axis. When surplus energy, such as an electric field for charging, is applied to these crystals at near room temperature or higher, the anions immediately begin to jump to their neighboring lattice sites, resulting in sufficiently rapid and large ionic conduction. The MEM analyses and density functional theory (DFT) calculations have revealed that the F- ions enable to easily travel along the ⟨110⟩ directions in the NaCl slabs of these crystals. These structural features thus make La1.2Sr1.8Mn2O7 and its fluorides possess both of two features incompatible with each other, ion storage and conduction, indispensable for rechargeable batteries.