Last Quarter

From Storm in Heaven:

Mizuki is a girl who wants to run away from her life. As she smiles at everything sad that happens to her, her soul becomes heavier day by day. Her escape door is Adam, an English singer. But is he really real, or is everything they've been through just a dream? Adam sees his dead Japanese girlfriend in Mizuki, but strangely, nobody, apart from a girl who met her at the gates of heaven, can see Mizuki. This is a story that takes place somewhere between dream and reality.