The invention provides an electrical energy storage module (100), comprising: at least one storage cell stack (10), comprising: a plurality of energy storage cells (1), which each have a cell housing (1a) each having two pole connections (1b,1c), wherein the energy storage cells (1) are arranged in series in the storage cell stack (10) in such a way that in each case a first pole connection (1b) and a second pole connection (1c) having different polarities of two adjacent energy storage cells (1) are galvanically connected to one another by means of flat cell connecting elements (4), wherein the cell housings (1a) of all of the energy storage cells (1) are galvanically connected to one another, wherein the first pole connection (1b) of an energy storage cell (1) arranged at a first end of the storage cell stack (10) is galvanically connected to the cell housing (1a), and wherein the second pole connection (1c) of an energy storage cell (1) arranged at a second end of the storage cell stack (10) and the cell housings (1a) each have a flat return conductor (5).