  The $\bar{B}_s^0 \to D_s^{(*)+} l^- \bar{\nu}_l$ semileptonic decays were
calculated in the framework of the standard model (SM) by employing the
perturbative QCD (pQCD) factorization approach. We defined four ratios of the
branching ratios of the considered decays $R(D_s^{(*)})$ and
$R_{D_s}^{l,\tau}$. From the numerical results and phenomenological analysis we
found that: (a) The pQCD predictions for the branching ratios $Br(\bar{B}_s^0
\to D_s^{(*)+} l^-\bar{\nu}_l)$ generally agree well with the previous
theoretical predictions; (b) For the four ratios, the pQCD predictions are
$R(D_s)= 0.392 \pm 0.022$, $R(D_s^{*})= 0.302\pm 0.011$,
$R_{D_{s}}^l=0.448^{+0.058}_{-0.041}$ and
$R_{D_{s}}^\tau=0.582^{+0.071}_{-0.045}$, which show a very good $SU(3)_F$
flavor symmetry with the corresponding ratios for $B\to D^{(*)} l^-
\bar{\nu}_l$ decays; and (c) we strongly suggest the measurements of the new
ratios $R(D_s^{(*)})$ and $R_{D_{s}}^{l,\tau}$ in the forthcoming Super-B
experiments.
