Tomorrow (Thursday) is the 7th of Adar (Zain Adar) and this date stands for the birthday and the Yahrzeit of Moshe Rabbeinu.
Talmud Megillah 13b teaches us that, first, Haman wished to destroy Mordechai alone but he changed his mind into destroying all the Jews. When Haman was casting the lots, he saw that the lot fell on the month of Adar. He thought that this would be a great sign, as Moshe had died in Adar. The month of Adar would not be an unlucky month for the Jews. However, Haman did not realize that while Moshe died on the seventh of Adar, he was also born on the seventh of Adar. Rashi commentates: Moshe's birth on that day compensated for the day's negative aspect of being the day of his death.
The Torah does not exactly tell us the date when Moshe died but Chazal figured it out be the days / time given when the Jews mourned Moshe (see the Book of Deuteronomy - Sefer Devarim 34:8).
Rabbi Shalom Arush writes in his book "The Garden of Emunah" about our mission in life:
"Each of us comes to this earth for the express purpose of fulfilling a mission. Some people enjoy a long life and others pass away at a young age. Our souls come to this earth for certain Tikkunim (soul rectifications) and others have to fulfill special tasks. The reason why some people live longer and others don't is beyond our understanding".
There is an opinion that, as soon as we fulfill our task in life, we pass away. I am not sure if this is always the case because the Arizal (Rabbi Yitzchak Luria) says in his book "Shaar HaGilgulim - The Gate of Reincarnations) that sometimes people soul's are reincarnated because they didn't fulfill a special task / rectification.
Obviously Moshe's task was fulfilled and he passed away. Nevertheless, it says that Meshiach's soul is going to have a spark of Moshe's.