A cooperative differential game of pollution control with non-zero absorption coefficient corresponding to the natural purification of the atmosphere for some enterprises based on data of Eastern Siberia region of the Russian Federation is considered. The property of strong time-consistency is determinative for multiple optimality principles in implementing of the solution. The core is used as a cooperative solution. The subset of the core is constructed that satisfies the above-mentioned property. The algorithm proposed in the paper [Petrosyan, Gromova, Pogozhev, 2016] is used for constructing the subset that allows to select functions which can be used as an imputation distribution procedure. It is also shown that the proportional solution belongs to the constructed subset.