The book was written by the son.
But because both father and son wrote a book about the same events using the same title at first glance it seemed like the son had plagiarized the father but after reading both it was obviously not.
The father died when his manuscript was half finished and his one was never published.
The son wrote and finished his own manuscript which was published and became a bestseller.
They were both (father and son) writing about what happened in their lives but from their own perspective.
The girl who the events were around then wrote a letter from her perspective (because she is not a writer).
So at the end there was:
1. A half written manuscript from the father from his perspective
2. Finished book by the son from his perspective
3. Letter by the lover girl from her perspective
Three different works all based on the same events by three different people. This is all explained in the manga.
who wrote the book?