  A cohomological criterion for the complete reducibility of modules of finite
length satisfying a composability condition for a meromorphic open-string
vertex algebra $V$ has been given by Qi and the author. In order to apply this
criterion, one needs to determine what types of $V$-modules satisfy the
composability condition. In this paper, we prove that the composability
condition is satisfied by generalized modules in a suitable category for a
grading-restricted vertex algebra satisfying natural conditions.
