  We propose a scheme to exchange optical vortices of slow light using the
phenomenon of electromagnetically induced transparency (EIT) in a four-level
double-$\Lambda$ atom-light coupling scheme illuminated by a pair of probe
fields as well as two control fields of larger intensity. We study the
light-matter interaction under the situation where one control field carries an
optical vortex, and another control field has no vortex. We show that the
orbital angular momentum (OAM) of the vortex control beam can be transferred to
a generated probe field through a four-wave mixing (FWM) process and without
switching on and off of the control fields. Such a mechanism of OAM transfer is
much simpler than in a double-tripod scheme in which the exchange of vortices
is possible only when two control fields carry optical vortices of opposite
helicity. The losses appearing during such OAM exchange are then calculated. It
is found that the one-photon detuning plays an important role in minimizing the
losses. An approximate analytical expression is obtained for the optimal
one-photon detuning for which the losses are minimum while the intensity of
generated probe field is maximum. The influence of phase mismatch on the
exchange of optical vortices is also investigated. We show that in presence of
phase mismatch the exchange of optical vortices can still be efficient.
