Jikan o Tomete Matteite (1985)

Set in the Wild West. 18-year-old Miriam has loved Douglas since she was 8, but he still sees her as a little girl (he’s 9 years older). Miriam goes missing on a trip and Douglas finally finds her, but she’s lost her memory. Douglas starts to realize his feelings for her when he’s frustrated that she doesn’t remember him, but first they have to deal with some murderous criminals before anything can be settled.

Source: www.anisearch.com/manga/3319