Even if no colonies get built, or only underground, I’d be in favor of just installing a huge solar powered blinking beacon on the moon that gets turned on when dark. Just a bit of “humanz was here” light graffiti.
It also seems logical that the best time to acknowledge this connection would be during eclipses, when both civilizations are looking most intently at each other. Perhaps the lights will blink in patterns, or form messages. Like a huge drone or stadium display 3/n