Weak marginality is quotient-transitive

This article gives the statement, and possibly proof, of a subgroup property (i.e., weakly marginal subgroup) satisfying a subgroup metaproperty (i.e., quotient-transitive subgroup property)
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Statement

Suppose $H\leq K\leq G$ are groups such that $H$ is a weakly marginal subgroup of $G$ and $K/H$ is a weakly marginal subgroup of $G/H$. Then, $K$ is a weakly marginal subgroup of $G$.

Proof

The proof idea is to substitute one word-letter pair inside the other.