The apparatus comprises a conveyor (2) for feeding paper sheets into a cassette (4) in a stacker (2). The conveyor (2) can be switched between two positions such that successive documents are separated from one another by a lateral shift. The cassette (4) is lowered in the stacker (3) as the stack builds up. After the stack is completed the cassette (4) is turned by 180°, removed from the stacker (3) and inserted into a sorter (6). The sorter (6) picks up the documents one by one and pushes them onto a conveyor (7) which transports them to a finishing machine (8).
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