CEP implies every relatively normal subgroup is weakly closed

This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., CEP-subgroup) must also satisfy the second subgroup property (i.e., subgroup in which every relatively normal subgroup is weakly closed)
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Statement

This has the following equivalent formulations:

• If $K$ is a CEP-subgroup of a group $G$, then $K$ is a subgroup in which every relatively normal subgroup is weakly closed.
• If $K$ is a CEP-subgroup of a group $G$, and $H$ is a normal subgroup of $K$, then $H$ is a weakly closed subgroup in $K$ with respect to $G$, i.e., any conjugate subgroup to $H$ in $G$ that is contained in $K$ must be contained in $H$ itself.