The selected shapes can be moved to a different layer as a whole. For this, choose "Change Layer" from the "Selection" submenu of the "Edit" menu. All selected shapes are moved to the layer that is the current one (marked with a rectangle) in the layer list. The shapes will not be moved across the hierarchy but just inside their cell.
All layers (source and target) must be located in the same layout. To move shapes to a different layout, use copy & paste.