  Within the Two Higgs Doublet Model (2HDM) with $\mathcal{CP}$ conservation
and a softly broken $Z_2$ symmetry, we analyze the flavor changing Higgs decays
$h\to bs$ ($bs$ refers jointly to the two decay channels $b\bar s$ and $\bar b
s$), where $h$ is identified with the SM-like Higgs boson discovered at the
LHC. We provide a comprehensive study of the decay width $\Gamma (h \to bs)$
with particular focus on the most relevant effects from the triple Higgs
coupling $\lambda_{hH^+H^-}$. Furthermore, we consider all the relevant
theoretical and experimental constraints to determine which predictions for the
$\mathrm{BR}\left(h\to bs\right)$ are still allowed by the current data. We
find that the predictions for $\mathrm{BR}\left(h\to bs\right)$ in types II and
III can be several orders of magnitude smaller compared to the SM value. In
contrast, in type I and IV we find that the predicted enhancements in the decay
rates with respect to the SM of up to about 70% and 50%, respectively, are
still allowed. We discuss how these deviations from the SM are caused by
interference effects controlled by the coupling $\lambda_{hH^+H^-}$ which can
be large for very heavy $H^\pm$. To better understand the role of
$\lambda_{hH^+H^-}$ in the $h \to bs$ decay we derive and analyze here the
analytical results for the $hbs$ one-loop effective vertex that is generated by
integrating out the heavy $H^\pm$.
