You should be able to run the "L/Mono" line-out into the subwoofer input (or the line-level input into the whole "home theatre" speaker system).
a) use the home theatre system, and turn off the AP-620 loudspeakers. That probably happens when you put a plug into the headphone jack. In that case, if you want to keep the stereo sound, run AP-620 "L/mono" into the HT "left" input, run "Right" into the HT "right" input. The HT will mix left and right, and send a mono signal to the subwoofer.
b) Use the AP-620 speakers and add the HT subwoofer. For that, run the AP-620 "L/mono" output into the HT input. Disconnect the high / midrange HT loudspeakers. Adjust the subwoofer volume with the HT "volume" control. That's the easiest way to use the HT strictly as a subwoofer.
What's the diameter of the AP-620 woofers? What's the power of the AP-620 amp?
PS -- since I don't have an AP-620, and don't have a HT system, you use these instructions at your own risk.
You'd need some way to kill the mi