Molten salts are crucial materials in energy applications, such as batteries, thermal energy storage systems or concentrated solar power plants. Still, the determination and interpretation of basic physico-chemical properties like ionic conductivity, mobilities and transference numbers cause debate. Here, we explore a method for determination of ionic electrical mobilities based on non-equilibrium computer simulations. Partial conductivities are then determined as a function of system composition and temperature from simulations of molten LiFαClβIγ (with α + β + γ = 1). High conductivity does not necessarily coincide with high Li+ mobility for molten LiFαClβIγ systems at a given temperature. In salt mixtures, the lighter anions on average drift along with Li+ towards the negative electrode when applying an electric field and only the heavier anions move towards the positive electrode. In conclusion, the microscopic origin of conductivity in molten salts is unraveled here based on accurate ionic electrical mobilities and an analysis of the local structure and kinetics of the materials.