Conjugate-dense sub-APS

Definition
A sub-APS $$H$$ of an APS of groups $$(G,\Phi)$$ is termed conjugate-dense if for every $$n$$, $$H_n$$ is conjugate-dense as a subgroup of $$G_n$$, i.e. for every $$n$$, every element of $$G_n$$ is conjugate (in $$G_n$$) to some element of $$H_n$$.