Nagai Yakusoku

One day, Marian, a duchess, rescues a man with amnesia. As if by fate, the two are drawn to each other and they vow to love and stay with each other forever. However, the day after their first night of intimacy, he disappears while going out to buy a ring. Saddened, Mariane heads for the royal capital on her mother's advice. There, she meets Prince Rufus, who bears a striking resemblance to Marian. The scar on the prince's arm is exactly the same as Marian. But she is afraid to confront the prince, who seems to have no memory of Marian...

(Source: Priere Bunko, translated)