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Using an inequality due to Ricard and Xu, we give a different proof of PaulSkoufranis's recent result showing that the strong convergence of possiblynon-commutative random variables $X^{(k)}\to X$ is stable under reduced freeproduct with a fixed non-commutative random variable $Y$. In fact we obtain amore 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 inmore striking language: the reduced free product is "continuous" with respectto strong convergence. The analogue for weak convergence (i.e. convergence ofall moments) is obvious. Our approach extends to the amalgamated free product,left open by Skoufranis.

Strong convergence for reduced free products (Remarks on a result by Paul Skoufranis)