Alexander was born on .12.1918, in Vinnytsia, Ukraine, to Miriam and Shlomo Wachter. In 1922, due to the growing Communist threat, the family moved to Bessarabia, which was under Romanian control, where his father dealt in metals. The family was Religious Zionist, and so he received a thorough Jewish education. At age eleven, he was sent to yeshiva in Kishinev and then to Iași. At the end of his studies, he received rabbinical ordination, but he did not make use of this certification. He studied in high school and he joined the Zionist youth movement HaShomer HaTza’ir, then Beitar. He eventually became the cell commander of the latter in Iași.
In 1937, he took part in the Af al Pi aliyah program, and he joined the Beitar company in Netanya; later, he joined the IZL. After some time, he was transferred to the Rosh Pina company. After an altercation between members of the company and some Arabs, he was arrested and sentenced to thirty days, as well as being forbidden to stay in the Galilee. At the end of this month, he joined the Beitar company in Ekron, in which he was appointed a company commander.
When the IZL split, he followed Yair, along with most of the company members. He arrived in Netanya a second time, and he was made the supervisor of Lehi in the area. About a year later, the Netanya police arrested him, apparently due to informers. That same evening, he managed to escape from the station. He hid for a few days in the orchards in the area. When he tried to reach Tel Aviv, he was identified and sent to prison once again. This time, he was transferred to Nablus, then to Jerusalem Central Prison, where he was tortured and humiliated. After two months, he was transferred to Acre Prison, then to Mizra and Latrun. In October 1944, he was one of the 251 to first be deported to Africa: first to Eritrea, then Sudan, then back to Eritrea, then to Kenya.
He arrived back in Israel on 12 July 1948, after years of imprisonment and exile. He joined the IDF and was assigned to the weapons company of Battalion 63. After his demobilization, at the end of 1949, he started studying law at Hebrew University. At the end of his studies, he went to work at the Ministry of Justice; from 1964 to 1976, he was the legal advisor of the Ministry of Industry and Trade. From 1976 to 1979, he was the consul for economic affairs in Canada, and afterwards the legal advisor for government trade in the Ministry of Industry and Trade. In 1994, he retired.
Throughout his life, he was dedicated to the study of the Land of Israel, as most of his free time was dedicated to Jewish studies and Jewish history.
In 1963, he married Rachel Lendner, whose family had lived in Jerusalem for generations. She also worked in the Ministry of Industry and Trade. They live in Jerusalem and have three children.