Isomorph-freeness is quotient-transitive

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

Statement with symbols

If $H\leq K\leq G$ are such that $H$ is an isomorph-free subgroup of $G$ and $K/H$ is an isomorph-free subgroup of $G/H$, then $K$ is an isomorph-free subgroup of $G$.