On sncc-inheritance of pointwise almost periodicity in flows

Let $H$ be a subnormal co-compact closed subgroup of a Hausdorff topological group $T$ and $X$ a compact Hausdorff space. We prove the inheritance theorem: A point of $X$ is almost periodic (a.p.) for $T\curvearrowright X$ iff it is a.p. for $H\curvearrowright X$. Moreover, if $T\curvearrowright X$ is minimal with $H⊲T$, then ${\mathcal{O}}_H\text{\hspace{0.17em}⁣}:X\to 2^X$, $x\mapsto \overline{Hx}$ is a continuous mapping, and, $T\curvearrowright X\mathrm{/}H$ is an a.p. nontrivial factor of $T\curvearrowright X$ iff $T\curvearrowright X\times T\mathrm{/}H$ is not minimal.