  The Scale Magnetic Effect (SME) is the generation of electric current due to
conformal anomaly in external magnetic field in curved spacetime. The effect
appears in a vacuum with electrically charged massless particles. Similarly to
the Hall effect, the direction of the induced anomalous current is
perpendicular to the direction of the external magnetic field $\bf B$ and to
the gradient of the conformal factor $\tau$, while the strength of the current
is proportional to the beta function of the theory. In massive electrodynamics
the SME remains valid, but the value of the induced current differs from the
current generated in the system of massless fermions. In the present paper we
use the Wigner--Weyl formalism to demonstrate that in accordance with the
decoupling property of heavy fermions the corresponding anomalous conductivity
vanishes in the large-mass limit with $m^2 \gg |e {\bf B}|$ and $m \gg |\nabla
\tau|$.
