So... is Hanbun no Tsuki ga Noboru Sora finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: February 24, 2006
Manga finished: November 27, 2006
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Yuuichi, a boy hospitalized with hepatitis A and frustrated with his confinement, finds his life changed when he encounters Rika, a beautiful girl also staying at the hospital.
Despite Rika's initially challenging personality, Yuuichi is drawn to her, and a bond begins to form between them.
The story follows their growing relationship as they experience the joys and difficulties of first love within the confines of the hospital, navigating their feelings amidst the shadow of Rika's serious illness.