Based on my experience, the best way to introduce two people on-line is as follows.
Person A, you work at XXX and I met you at XXX. We did this together.
Person B, you like XXX music, you work at XXX and we met at XXX.
I think you two would benefit from knowing eachother because XXX.
It is courteous for the first responder to Reply-to-All and include the introducer in his communication with the new friend. For example, if I introduced Dan and Amanda, then I would like to see their first message carbon copy me.
Nick - thanks for the introduction!
Amanda - I live near the XXX - maybe we could meet up for coffee sometime? Give me a call... Dan
I have not made a lot of email introductions in my life - maybe a dozen or two. But if I do not get included in the initial reply back, it could be my last introduction for those people.
Why? Because I am nosy. That is the main reason.
Bonus points if you include me in the second email message, but under no circumstances would I want to be included in the third or further conversation between the parties. And EXTRA bonus points if you call and ask me if it is OK if you two start dating. (You know who you are!) Stay classy.