to have them observe the fourteenth and the fifteenth day of the month of Adar each year

So Queen Esther, the daughter of Abihail, and Mordecai the Jew wrote with full authority to confirm this second ¹  letter about Purim.

to establish these days of Purim in their proper times, just as Mordecai the Jew and Queen Esther had established, and just as they had established both for themselves and their descendants, matters pertaining to fasting and lamentation.