This paper develops a strategy, using concepts from Mean Field Games, to coordinate the charging of a large population of battery electric vehicles (BEVs) in a parking lot powered by solar energy and managed by an aggregator. The goal is to share the energy available so as to minimize the standard deviation of the state of charge (SoC) of batteries at the end of the day. We consider both cases of homogeneous and heterogeneous populations of BEVs with a stochastic dynamics of SoC. The charging laws correspond to the Nash equilibrium induced by quadratic cost functions based on an inverse Nash equilibrium concept and designed to help the batteries with the lowest initial SoCs. While the charging laws are strictly decentralized, they guarantee that a weighted mean of instantaneous charging powers to the vehicles follows a mean charging trajectory based on the solar energy forecast for the day. That day ahead forecast is broadcasted to the vehicles which can then gauge the necessary SoC upon leaving their home. We illustrate the advantages of our strategy in the two cases of a typical sunny day and a typical cloudy day when compared to more straightforward strategies: first come first full and equal sharing.