  We consider transfer of optical vortices between laser pulses carrying
orbital angular momentum (OAM) in a cloud of cold atoms characterized by the
$\Lambda$ configuration of the atom-light coupling. The atoms are initially
prepared in a coherent superposition of the lower levels, creating a so-called
phaseonium medium. If a single vortex beam initially acts on one transition of
the $\Lambda$ scheme, an extra laser beam is subsequently generated with the
same vorticity as that of the incident vortex beam. The absorption of the
incident probe beam takes place mostly at the beginning of the atomic medium
within the absorption length. The losses disappear as the probe beam propagates
deeper into the medium where the atoms are transferred to their dark states.
The method is extended to a tripod atom-light coupling scheme and a more
general $n+1$-level scheme containing $n$ ground states and one excited state,
allowing for creating of multiple twisted light beams. We also analyze
generation of composite optical vortices in the $\Lambda$ scheme using a
superposition of two initial vortex beams and study lossless propagation of
such composite vortices.
