Dr. A. Hillman corresponded with the Rebbe in the 1940s, in the years before the Rebbe's leadership, raising questions of Torah scholarship. No reliable published biography is available; the summary below is drawn from the letters themselves.
The Rebbe's letters answer his questions on Tanya chapter 32 — the command to love every Jew, the categories of sinners to whom it does not apply, and the halachic distinctions involved (IK 244, 267). Other letters explain phrases and customs of the prayers (IK 293), the correct text and interpretation of the piyut Yoshevei Keranos (IK 428), and seder customs, the structure of the Haggadah and the acceptance of the Torah (IK 383). One letter accompanies the Haggadah sent to him, with comments on the journal Sinai and on library subscriptions (IK 317).
See also: Torah study – The Rebbe's answers on verses, Rashi, Gemara and Midrash; Leadership – Jewish unity and Ahavas Yisrael.