  Improving the beginning steps of a previous work, we settle the dual
embedding method (DEM) as an alternative and efficient method for obtaining
dual equivalent actions also in D=3. We show that we can obtain dual equivalent
actions which were previously obtained in the literature using the gauging
iterative Noether dualization method (NDM). We believe that, with the
arbitrariness property of the zero mode, the DEM is more profound since it can
reveal a whole family of dual equivalent actions. After a review of our
previous work, we obtain the dual equivalent theory of the self-dual model
minimally coupled to U(1) charged bosonic matter. The result confirms the one
obtained previously which is important since it has the same structure that
appears in the Abelian Higgs model with an anomalous magnetic interaction.
