  Let $A$ be a simple separable nuclear C$^*$-algebra with a unique tracial
state and no unbounded traces, and let $\alpha$ be a strongly outer action of a
finite group $G$ on $A$. In this paper, we show that $\alpha\otimes
\mathrm{id}$ on $A\otimes\mathcal{W}$ has the Rohlin property, where
$\mathcal{W}$ is the Razak-Jacelon algebra. Combing this result with the recent
classification results and our previous result, we see that such actions are
unique up to conjugacy.
