Like @michaelahess is saying, J3 is looking for dry contacts (no AC power). So if you use the existing wall switch location you must locate the incoming power to your switch/outlets which could be up at one of the outlets at the cabinets or at the switch to disconnect which would allow you to re do the wiring for contact control. Certainly possible but it will take some time and effort to trace all this out and convert the existing wiring from 120 use case to simply being dry contact use back to an H801. All that to say I think you might want to reconsider an alternate way to solve your problem.
I have a similar layout with three cabinet lighting outlets above three separate cabinet locations all controlled by one switch. My cabinets locations are all separated so it was easiest for me to install three separate H801’s at each of the outlet locations above the cabinets. Instead of converting my existing power outlets wiring I just replaced the dumb wall switch with a smart switch. I monitor the smart switch with Smart Lighting smartapp to trigger all three H801 on/off. If you use a smart dimmer switch you could potentially even set the levels of light levels of the H801 using the smart dimmer switch via smartapp like @ady624 CoRE. Or use a smartapp like @Kriskit Trend Setter to sync all three together from a manual setting and a smart switch.