WhatsApp conversation with an overseas person on their Shabbat

Isn't there also a problem here with enjoying someone else's Shabbat act?

And maybe there is also a kind of prohibition against speaking to a foreigner here?

I don't think so. The brother does this for himself and not for him. And in the prohibition of saying something to a non-believer, there is simply no prohibition when the saying is said in a secular context (except according to Rashi's view, the prohibition of saying something is from the point of view of sending a message to a non-believer, to be more serious. And the Jews did not take this seriously, because in a Jew there is no messenger to speak an offense. Although, in my view, it is necessary to discuss whether in a Jew who does not believe there is a messenger to speak an offense. It seems to me that in a simple way, there is no, and one must be careful about this).

The title doesn't really reflect the question.

You wrote “If he doesn't believe in Halacha at all (and not just doesn't observe mitzvot) then in my personal opinion there is no problem because his offenses are not offenses”
What do you mean? That since he doesn't believe at all, then it's not appropriate to talk to him about what is permitted and what is prohibited?

If we borrow this from civil law, then for example: is it like we can't tell a Neturi Karta man to abide by the laws of the state when he doesn't even agree with its very existence??
But the bottom line is that in civil law we would punish such a person even if he doesn't recognize our authority.

In short, what is the rabbi's explanation for his idea??

It has nothing to do with civil law. In civil law, commandments do not require intention or faith. The concern of the law is not the work of the legislator, but rather the maintenance of order and the fulfillment of obligations. In halacha, its concern is the work of the ’ and not a collection of acts done by the individual.
Regarding the commandment of needing faith, see my article here:
https://mikyab.net/%D7%9B%D7%AA%D7%91%D7%99%D7%9D/%D7%9E%D7%90%D7%9E%D7%A8%D7%99%D7%9D/%D7%91%D7%A2%D7%A0%D7%99%D7%99%D7%9F-%D7%94%D7%9B%D7%A9%D7%9C%D7%AA-%D7%97%D7%99%D7%9C%D7%95%D7%A0%D7%99-%D7%91%D7%A2%D7%91%D7%99%D7%A8%D7%94