  Let $\mathcal{C}$ be a unital C$^*$-algebra and $E_n$ be the Hilbert
$\mathcal{C}$-module defined as the completion of the $\mathcal{C}$-valued
Schwartz function space $\mathcal{S}^\mathcal{C}(\mathbb{R}^n)$ with respect to
the norm $\|f\|_2 := \left\| \int_{\mathbb{R}^n} f(x)^*f(x) \, dx
\right\|_\mathcal{C}^{1 / 2}$. Also, let $\text{Ad }\mathcal{U}$ be the
canonical action of the $(2n + 1)$-dimensional Heisenberg group by conjugation
on the algebra of adjointable operators on $E_n$ and let $J$ be a
skew-symmetric linear transformation on $\mathbb{R}^n$. We characterize the
smooth vectors under $\text{Ad }\mathcal{U}$ which commute with a certain
algebra of right multiplication operators $R_h$, with $h \in
\mathcal{S}^\mathcal{C}(\mathbb{R}^n)$, where the product is "twisted" with
respect to $J$ according to a deformation quantization procedure introduced by
M.A. Rieffel. More precisely, we establish that they coincide with the
corresponding algebra of left multiplication operators, as conjectured by
Rieffel.
