  Recently, some S-stars (S4711, S62, S4714) orbiting the supermassive black
hole (SMBH) in Sgr A$^\ast$ with short orbital periods ($7.6\,\mathrm{yr}\leq
P_\mathrm{b}\leq 12\,\mathrm{yr}$) were discovered. It was suggested that they
may be used to measure the general relativistic Lense-Thirring (LT) precessions
of their longitudes of ascending node $\mathit{\Omega}$ induced by the SMBH's
angular momentum $\boldsymbol{J}_\bullet$. In fact, the proposed numerical
estimates hold only in the particular case of a perfect alignment of
$\boldsymbol{J}_\bullet$ with the line of sight, which does not seem to be the
case. Moreover, also the inclination $I$ and the argument of perinigricon
$\omega$ undergo LT precessions for an arbitrary orientation of
$\boldsymbol{J}_\bullet$ in space. We explicitly show the analytical
expressions of $\dot
I^\mathrm{LT},\,\dot{\mathit{\Omega}}^\mathrm{LT},\,\omega^\mathrm{LT}$ in
terms of the SMBH's spin polar angles $i^\bullet,\,\varepsilon^\bullet$ by
finding the range of values for each of them in arcseconds per year
($^{\prime\prime}\,\mathrm{yr}^{-1}$). For each star, the corresponding values
of $i^\bullet_\mathrm{max},\,\varepsilon^\bullet_\mathrm{max}$ and
$i^\bullet_\mathrm{min},\,\varepsilon^\bullet_\mathrm{min}$ are determined as
well, along with those $i_0^\bullet,\,\varepsilon_0^\bullet$ that cancel the LT
precessions. The LT perinigricon precessions $\dot\omega^\mathrm{LT}$ are
overwhelmed by the systematic uncertainties in the Schwarzschild ones due to
the current errors in the stars' orbital parameters and the mass of Sgr
A$^\ast$ itself. [Abridged]
