CEP implies every relatively normal subgroup is weakly closed

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.