  Using an inequality due to Ricard and Xu, we give a different proof of Paul
Skoufranis's recent result showing that the strong convergence of possibly
non-commutative random variables $X^{(k)}\to X$ is stable under reduced free
product with a fixed non-commutative random variable $Y$. In fact we obtain a
more general fact: assuming that the families $X^{(k)}=\{X_i^{(k)}\}$ and
$Y^{(k)}=\{Y_j^{(k)}\}$ are $*$-free as well as their limits (in moments) $X
=\{X_i \}$ and $Y =\{Y_j\}$, the strong convergences $X^{(k)}\to X$ and
$Y^{(k)}\to Y$ imply that of $\{X^{(k)},Y^{(k)} \}$ to $\{X ,Y\}$. Phrased in
more striking language: the reduced free product is "continuous" with respect
to strong convergence. The analogue for weak convergence (i.e. convergence of
all moments) is obvious. Our approach extends to the amalgamated free product,
left open by Skoufranis.
