Moshe’s birthday and Yartzite:
Moshe Rabbeinu was born and passed away on Zayin Adar. One is to increase in joy on this day. Some are accustomed to fast. This is not the Chabad custom. However one should increase in charity on this day in exchange for the fast. Some do not say Tachanun on this day.
Moshe’s birthday and Yartzite on a leap year: In a leap year, Moshe’s birthday and Yartzite are [Halachically] commemorated on the 7th of Adar I. However, the spiritual aspect behind the auspicious day applies to both 7th of Adar I and 7th of Adar II.
 Gemara Sota 12b
Was Moshe born during a leap year? The Gemara records a dispute on this matter: Some say Moshe was born on Adar Rishon of a leap year. Others say he was born in a regular year with a single Adar. [Sota ibid]
On which weekday, and at what time, did Moshe pass away? Moshe passed away on Shabbos afternoon, towards the time of Mincha. [Admur 292:5; Bach 292:2; Zohar Chadash 156a]
Did Moshe pass away during a leap year? The M”A 580:20 brings a dispute on this matter. The Terumos Hadeshen 294 writes Moshe passed away in a regular year that contained one Adar. However, the Yalkut Yehoshua writes that there are opinions who say Moshe Rabbeinu passed away during the first Adar of a leap Year. According to the opinion in the Gemara that Moshe Rabbeinu was born on Adar Rishon one must conclude that he also passed away on Adar Rishon, as it states regarding Moshe that Hashem filled his years that he lived an exact number of years. [Sheilas Yaavetz 1:117; Likkutei Sichos 16 p. 344 footnote 40]
Other Opinions: Some opinions say that Moshe passed away on the 7th of Shevat. [brought in M”A 580:20] The Midrash states that Moshe was born and passed away on the first of Adar. [Esther Raba 16] However the Anaf Yosef attributes this to a misprint and it should read the 7th of Adar, as stated in the Talmud.
 Hisvadyos 1988 2 p. 388 [printed in Shaar Hamoadim Adar 17] The Rebbe there states as follows: It is found that Chassidim do not mark this day with any special event. This is puzzling. Hence one is to mark it with increase in joy as is befitting of the Yom Hahilula of a Tzaddik, and especially Moshe Rabbeinu. Likewise, it is also his birthday, thus giving a double reason to celebrate. [Rebbe ibid] On another occasion the Rebbe stated that it should have been proper to establish the joy of this day similar to the celebration that is accustomed on Lag Baomer. [Sichas listed in Otzer Minhagei Chabad 28]
 Michaber 580:2
 As Chassidim are accustomed to not increase in fast days. [Rebbe in Shaar Hamoadim ibid; Sichas listed in Otzer Minhagei Chabad 28]
 Rebbe ibid
 The Chabad Rabbeim did not say Tachanun on Zayin Adar starting from the Mincha of Vav Adar. Nevertheless, this custom only began once they took leadership of the movement and not beforehand. [Sefer Haminhagim [English] p. 168]
The reason: As the soul of Moshe shines within the leader of each generation, and hence they feel the value of the birth of Moshe on this day. [Likkutei Sichos 16 p. 350-351]
 Likkutei Sichos 15 Tetzaveh footnote 8 and 63
 Magen Avraham 580:8; Teshuvos Mahril 31; Terumos Hadeshen 244; Rama 568:7; Aruch Hashulchan 580:3; Mishneh Berurah 580:15; Orchos Chaim; Likkutei Sichos 16 p. 344 footnote 39: This is the final ruling, as the majority of Jewry lived in their provinces and testified this to be the custom.
Other Opinions: Some Poskim hold that during a leap year Moshe’s Yartzite is to be commemorated on Zayin Adar II. [Chacham Tzevi, brought in Sheilas Yaavetz 1:117; Siddur Yaavetz; Chasam Sofer 163; Vayaan Yitzchak 39].
Did Moshe pass away during a leap year? The M”A 580:20 brings a dispute in this matter. The Terumos Hadeshen 294 writes that Moshe passed away in a regular year that contained one Adar. However, the Yalkut Yehoshua writes that there are opinions that say Moshe Rabbeinu passed away during the first Adar of a leap Year. According to the opinion in the Gemara that Moshe Rabbeinu was born on Adar Rishon one must conclude that he also passed away on Adar Rishon, as it states regarding Moshe that Hashem filled his years that he lived an exact amount of years. [Sheilas Yaavetz 1:117; Likkutei Sichos 16 p. 344 footnote 40]
 Regarding fasting and Tachanun on the day of his Yartzite. See previous Chapter Halacha 3
 Such as the Simcha. This is opposed to the Halachic aspect, such as fasting, which is to be done [by those accustomed to do so] in Adar I, as ruled by the Poskim mentioned above.
 Sichas 1992 2 p. 721, brought in Shaareiy Hamoadim Adar 19