  In this work we study the quasi-two-body decays $B\to K^*\gamma\to
K\pi\gamma$ in the perturbative QCD (PQCD) approach. The two-meson distribution
amplitudes (DAs) are introduced to describe the final state interactions of the
$K\pi$ pair, which involve the time-like form factors and the Gegenbauer
polynomials. We calculate the CP averaged branching ratios for the decays
$B_{(s)}\to K^*\gamma\to K\pi\gamma$. Our results are in agreement with the new
update data measured by Belle II, which suggests these quasi-two-body decays
are more appropriate to be analyzed in three-body framework than in the
two-body one. We also predict the direct CP-violation asymmetries for the
considered decay modes and find that $A_{CP}(B_{u,d}\to K^*\gamma\to
K\pi\gamma)$ is small and less than $1\%$ in magnitude, while $A_{CP}(B_{s}\to
K^*\gamma\to K\pi\gamma)$ is larger and can arrive at a few percent. Our
predictions can be tested by the future B meson experiments.
