Rinni is the daughter of Neo-Queen Serenity and King Endymion in the future Tokyo. She goes back in time to find the silver crystal so she can save her mother in Sailor Moon R. Right when Serena and Darien are about to kiss, Rinni falls from the sky and steals Darien's kiss from Serena. Rinni stays at Serena's house and makes it so Serena's family thinks she is Serena's cousin(I think its cousin..)
Rinni turns to Wicked Lady later in Sailor Moon R, which you can find out more about at my Wicked Lady page, which will be up ASAP.
Sometime in Sailor Moon Super S Rinni and Serena switch places and Serena ends up a little girl and Rinni a teenager.
