In Another World, My Sister Stole My Name

Through a handheld mirror connected to another world, college student Ichika befriends a boy named Cecil. But when the mirror disappears one day along with her older sister, Karen, Ichika thinks she'll never see the two of them again…until a year later, when the mirror suddenly turns up and sends Ichika to the world on the other side! There, she finds a grown-up Cecil and her sister, who, for some reason, has become a saint named Ichika—?! After Karen has stolen her name and life, Ichika must forge her own destiny in this otherworldly, doting fantasy! 

(Source: Yen Press)