Wrappings (17) of substantially parallelepiped shape, each fashioned from at least one packaging component (6, 7, 11, 12, 13, 16) and presenting two portions overlapped and fixed along at least one face, are transferred by a device making use of a reciprocating pusher (65) equipped with a head (67) offered to the face of the wrapping (17) presenting the overlapped portions. During each active stroke of the pusher, a wrapping (17) is directed from a first position to a second position. The transfer device comprises a pneumatic circuit (70) producing jets of air directed at the face of the wrapping that coincides with the area of contact between the two overlapped portions, at least at the moment of inversion when the active stroke of the pusher (65) terminates and the return stroke commences.