Ane no Kawari ni, Yomei Ichinen to Iwareru Koushaku Shisoku-sama to Konyaku suru Koto ni Narimashita

Edith is an orphaned girl who is treated coldly by her adoptive parents and sister. One day, her adoptive sister is offered a marriage proposal to Lionel, the eldest son of the Marquis of Granville, a very prestigious family. However, there is a reason for this proposal... so Edith becomes engaged to him instead of her sister. "I'm sorry, I can't believe you're engaged to me like this. Can you just bear with me for one year?" Her fiancé has only one year to live, but pure love brings about a miracle in this happy love story! (Source: Kodansha, translated)