  Given a graph of groups $\mathcal{G} = (\Gamma, \{G_v\}, \{G_e\})$ with
certain conditions on vertex groups and $G$ acts acylindrically on its
Bass-Serre tree $T$. Let $H$ be a finitely generated subgroup of $G$. We prove
the following statements equivalence: $H$ has finite height, $(G, T, H)$ is a
$A/QI$--triple, $H$ is strongly quasiconvex and virtually free in $G$. We also
give a condition to determine whether strong quasiconvexity in a group is
preserved under amalgams.
