K-cup,
Correction/clarification: My husband just told me that from when the Lubavitcher Rebbe arrived in America in 1941 until he took the leadership and became the Lubavitcher Rebbe in 1950, he and Rabbi Hutner maintained a weekly chavrusa (joint study).
The Rosh Yeshiva maintained an on-going correspondence with the Rebbe. Some of the response letters of the Rebbe are printed in Igros Kodesh Volumes 7- pp. 2, 49, 192, 215, 12- pp. 28, 193, 14- pp. 167, 266, 18- pp. 251, 25- pp. 18–20, and 26- p. 485.
The Rosh Yeshiva (in these letters) is seeking the Rebbe’s views on a specific questions in halacha, queries about kabbalistic topics, and also asking for his brocha.
The letters sent by the Rosh Yeshiva are also printed in Mibeis Hagenozim, S.B. Levine, Kehot 2009, pp. 88–98.
When we see the tremendous respect each of these Gedolim had for each other (even though they did NOT agree with each other and criticized each other’s ways), it magnifies my pain when the students of each these giants demonstrate a lack respect for the other Gadol.