Q. If we celebrate zain Adar, the yortzait of Moshe Rabenu on the second Adar, why do we read parshas Tetzave, where his name is omitted on the first Adar?
A. Remoh (O.H. 568: 7) quoting Maharil and Mahari Mintz, rules that in regards to a common yortzait, the custom is to fast on the first Adar. However, Bais Yisroel (92) maintains that the yortzait of Moshe Rabeinu is observed on the second Adar. His reasoning is based on Talmud (Meggila 13b) that relates the miracle of Purim to the yortzait of Moshe Rabeinu and since Purim is celebrated on the second Adar so is his yortzait. Hilchos K'tanos (2: 173) also maintains that it is kept on the second Adar since our sages teach that, Hashem fulfills the years of the just until the last day (Rosh Hashana 11a), if the year he past away was a leap year, it would have occurred on the second Adar. (See also Yaaros D'vash 2 p. 140 and Shilas Yavetz 1: 117))
Horav Shlomo Miller Shlit'a pointed out, that although it is custom for the chevra kadisha societies to fast and commemorate their traditional seudah on the seventh day of second Adar, Mishna Berura (580; 15) mentions that the fasting for Moshe Rabeinu's yortzait is on the first Adar.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a