  The rare cascade $B_{s}$ ${\to}$ ${\phi}f_{0}(980)$ ${\to}$
${\phi}\,{\pi}^{+}{\pi}^{-}$ decay is studied with the perturbative QCD
approach based on the formula for the quasi two-body decay, where the two-pion
pair originates from the $S$-wave resonant $f_{0}(980)$ state. It is found that
with the introduction of the nonperturbative two-pion distribution amplitudes
and the Flatt\'{e} parameterization of the scalar form factor for the
$f_{0}(980)$ resonance, the branching ratio in the mass range 400 MeV $<$
$m({\pi}^{+}{\pi}^{-})$ $<$ 1600 MeV is ${\cal B}_{\rm theo}(B_{s}^{0}\,
{\to}\,{\phi}\,f_{0}(980)\,{\to}\,{\phi}\,{\pi}^{+}\,{\pi}^{-})$ $=$
$[1.31_{-0.31}^{+0.40}(a_{{\pi}{\pi}}){}_{-0.16}^{+0.19}(m_{b})
{}_{-0.09}^{+0.10}(\text{CKM})]{\times}10^{-6}$, where the uncertainties come
from the parameter $a_{{\pi}{\pi}}$ of the two-pion distribution amplitudes,
the $b$ quark mass $m_{b}$, the Cabibbo-Kobayashi-Maskawa (CKM) factors,
respectively. This result agrees with the recent LHCb measurement within
uncertainties, ${\cal B}_{\rm exp}(B_{s}^{0}\,{\to}\,{\phi}\,
f_{0}(980)\,{\to}\,{\phi}\,{\pi}^{+}\,{\pi}^{-})$ $=$
$(1.12{\pm}0.16^{+0.09}_{-0.08}{\pm}0.11){\times}10^{-6}$, where the errors are
statistical, systematic and from the normalization, respectively.
