  We extend our recent works on the two-pion $S$-wave resonance contributions
to the kaon-pion ones in the $B$ meson hadronic charmonium decay modes based on
the perturbative QCD approach. The $S$-wave $K\pi$ time-like form factor in its
distribution amplitudes is described by the LASS parametrization, which
consists of the $K^*_0(1430)$ resonant state together with an effective range
nonresonant component. The predictions for the decays $B\rightarrow J/\psi
K\pi$ in this work agree well with the experimental results from $BABAR$ and
Belle Collaborations. We also discuss theoretical uncertainties, indicating the
results of this work, which can be tested by the LHCb and Belle-II experiments,
are reasonably accurate.
