The schools of Shammai and Hillel for the very first time disagreed regarding a case of Jewish law. This occurred around the turn of the 1st century. In the ensuing generations, the schools argued regarding many different laws, until the law was established according to the teachings of the "House of Hillel" -- with the exception of a few instances. According to tradition, following the arrival of the Moshiach the law will follow the rulings of the House of Shammai.

All throughout, the members of the two schools maintained friendly relations with each other.

Link: Houses of Shammai & Hillel

After a 12-day sea voyage, the previous Lubavitcher Rebbe, Rabbi Yosef Yitzchak Schneersohn (1880-1950), disembarked at the New York harbor on the 9th of Adar II of 1940, following his miraculous rescue from Nazi-occupied Warsaw.

Link: Vintage film clip of the Rebbe's arrival in NY, March 19, 1940; more about Rabbi Yosef Yitzchak of Lubavitch.