  In this paper, we show that the strong embeddability has fibering permanence
property and is preserved under the direct limit for the metric space.
Moreover, we show the following result: let $G$ is a finitely generated group
with a coarse quasi-action on a metric space $X$. If $X$ has finite asymptotic
dimension and the quasi-stabilizers are strongly embeddable, then $G$ is also
strongly embeddable.
