A device for handling/stacking flexible sheets is described that includes: a box-shaped body having an inlet area and an outlet area; a helical conveying element for the flexible sheets, housed in the box-shaped body and extending between the inlet and outlet areas; and a drive assembly connected to the helical conveying element and configured to drive it around a rotation axis. The helical conveying element includes a helical thrust wall, wound helically about the rotation axis and having a thrust surface wound helically about the rotation axis, which, because of the rotation of the helical conveying element about the rotation axis, contacts/pushes the flexible sheets towards the outlet area. The helical conveying element includes a stiffening wall, which protrudes from the thrust wall away from the thrust surface and is wound about the rotation axis for at least one winding section of the thrust wall about the rotation axis.