Periodic groups saturated by the group $U_3(9)$

Let $\mathfrak{M}$ be a set of finite groups. A group $G$ is said to be saturated by $\mathfrak{M}$, if every finite subgroup of $G$ is contained in a subgroup isomorphic to a group from $\mathfrak{M}$. We prove that a periodic group saturated by set consisting of the single finite simple group $U_3(9)=PSU_3(81)$ is isomorphic to $U_3(9)$.