John Gill Commentary Esther 9:20

"And Mordecai wrote these things, and sent letters unto all the Jews that were in all the provinces of the king Ahasuerus, both nigh and far," — Esther 9:20 (ASV)

And Mordecai wrote these things
The transactions of those two days, and the causes of them, as well as the following letter; some conclude from hence that he was the penman of the book; and so he might be, but it does not necessarily follow from hence:

and sent letters unto all the Jews that were in all the provinces of
the King Ahasuerus, both nigh and far ;
such as were near the city Shushan, and those that were at the greatest distance from it; these were more especially the things he wrote.