The module (2) has a storage area comprising a splitting knife (18) with which two forces exercised antiparallel to a stacking direction (34) of a part of a mail piece (P1) stored in the area during existence of an establishing function, respectively. A feed stop (14) is moved in the stacking direction for producing a pull-off opening (16). The splitting knife is driven by an underfloor belt or separately, where one of the forces is adjusted based on a characteristic of an actually stored mail piece.