Hi Nicolas.
This isn’t a built-in feature, but I’ve heard of a plugin for duplicating TEC events: https://wordpress.org/plugins/duplicate-tec-event/ (third-party, not guaranteed or supported by us)
You might be able to use it (or at least reference its code) to come up with something for your multisite setup.
Or, even easier, you might be able to just oEmbed the actual event, which should auto-link it to where you want it to go anyway!
Please let me know how things go for you, and please include a link to your event if you do request additional assistance.
Thanks!