As “the book” elsewhere in Esther always means a particular book - “the book of the chronicles of the kings of Media and Persia” - Esther 2:23; Esther 6:1; Esther 10:2 it seems best to give it the same sense here.
Related Commentaries of Esther 9:32
Esther 9:32
32 And the decree of Esther confirmed these matters of Purim; and it was written in the book.