  In this article we establish that in the superdiffusive regime $1/2 < p < 1$
the fluctuations of a general step-reinforced random walk around $n^p \hat{W}$,
where $\hat{W}$ is a non-degenerate random variable, is Gaussian. This extends
a known result, by Kubota and Takei for the elephant random walk, to the more
general setting of step-reinforced random walks. Further, we show an
application of said fluctuation result to reinforced empirical processes, which
yields a refined Donsker's invariance principle for the superdiffusive regime.
