  Under full H\"ormander's conditions, we prove the strong Feller property of
the semigroup determined by an SDE driven by additive subordinate Brownian
motion, where the drift is allowed to be arbitrarily growth. For this, we
extend a criterion due to Malicet-Poly \cite{Ma-Po} and Bally-Caramellino
\cite{Ba-Ca} about the convergence of the laws of Wiener functionals in total
variations. Moreover, the example of a chain of coupled oscillators is
verified.
