Is there any Outlook (I use version 2016) plug-in or something to achieve that? I browsed for solution, but to no avail. After all these two pieces of software come from the same company and it is logical to expect them to work in concert.
I know that it works the other way around, user may choose to receive e-mail message about missed Teams’ conversations, but this is not what I am interested in.
Based on my experience, maybe you could try to create a flow with Outlook and teams via Power Automate like below, you could design it for your need(log in your office.com> search for power automate app>create new auto folow):