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

Let $X$ be a regular laterally complete $C_\infty(Q)$-module and $\mathcal{B}$ 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 $\mathcal{B}$ and set of pairwise different cardinal numbers. It is proved that $C_\infty(Q)$-modules $X$ and $Y$ are isomorphic if and only if $\Gamma(X) = \Gamma(Y)$.