Another question about integration between Teams and Skype for Business

Earlier I asked a question about Using Teams as my chat app for Office and Skype of Business. That question was answered and I thought that would be the end of it.

But I'm wrong. Today my colleague is wondering why he doesn't see my status in Skype for Business. (He's the one who believes that Skype for Business is the perfect chat client - superior in all ways when compared to Teams or any other chat client.) I'm no longer using Skype for Business, thinking that since I've switched to using Teams instead for chat (and having set the relevant setting to that effect), that would be the end of it. I could chat with them, they can chat with me, etc. But my colleague doesn't see me as being available in Skype for Business. Why is that? Is the status of one (Teams) totally irrelevant to the other?