I heard from Rabbi Moshe Rosenman Shlita (Rebbe in Yeshivas Derech Chaim in Brooklyn, NY) that after the defeat of Amalek we find the acceptance of converts. Two instances of this phenomenon is after the first battle with Amalek, Yisro converted, and in the Megillah we find that after Haman and other Amalekites were killed, many from among the people of the land professed themselves Jews (Esther 8:17). On an apparently unrelated note, the Sfas Emes writes that Amalek was against Torah, and therefore following the first battle of Amalek, the Jewish People received the Torah. In a similar vein, the Sfas Emes writes, after defeating Amalek in the days of Mordechai and Esther, the Jewish People once again reaccepted the Torah (See Shabbos 88a).
We can offer the following explanation that will demonstrate an association between the idea that after the defeat of Amalek there was an acceptance of converts and a reacceptance of Torah. The word for convert is גר, which using א”ת ב”ש is רג, the same letters. The Megillah is referred to as אגרת, and the א”ת ב”ש is תרגא, the same letters. Perhaps we can suggest that a convert has only himself, with no obstacles and no lineage. Thus, the convert is the embodiment of truth, as he has “no baggage.” In a similar vein, the Megillah is referred to in the Gemara (Megillah 16b) as אמיתה של תורה, the truth of Torah. Thus, the Megillah is the truth, and that is why the word used to describe the Megillah is אגרת, which in א”ת ב”ש is תרגא, the same exact letters. This reflects on the idea that the Megillah, like Torah, is true inside and out. (The concept that is introduced here is that when a word contains the same letters in א”ת ב”ש, that is a hint that the deeper meaning of that word is truth).