Laterally complete $C_\infty(Q)$-modules

Let $X$ be a regular laterally complete $C_\infty(Q)$-module and $\mathscr B$ be a Boolean algebra whose Stone space is $Q$. We introduce the passport $\Gamma(X)$ for $X$ consisting of uniquely defined partition of unity in $\mathscr B$ and set of pairwise different cardinal numbers. It is proved that $C_\infty(Q)$-modules $X$ and $Y$ are isomorphic if and only if $\Gamma(X)=\Gamma(Y)$.