Found shared account? What do I do next?

Is it just friends sharing? If so, why do you care? It's like reporting your neighbor for jaywalking. Yeah, it's "illegal"...

Or, is it account or elo boosting? Intentionally designed to malign the system?

Are they using scripts? Are they sharing it as a troller account to destroy other people's games? Are they using this extra account for some kind of specific malfeasance?

Consider the reason. And if it's truly serious, try to contact Riot personally.

Well... the simplest way is by reporting them after playing a match with them. But other than that, you can report them via a ticket to player support. However, if you do send a ticket in, be aware that Player Support will not discuss how they handle the ticket with you. They will simply thank you for the effort you have made to keep League an honest and fair game, and handle matters from there in private.

Wow man are you for real? stay in your lane