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Moshe’s birthday and Yartzite on a leap year:
On a leap year Moshe’s birthday  and Yartzite are [Halachicly] 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.
List of coming leap years
|Hebrew Year||Secular Year|
 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