I could not identify Rabbi Avraham Stern with certainty from published sources; this summary is drawn from the Rebbe's letters to him, which span about two decades (roughly 5708–5729, 1948–1969) and show him to be a Torah scholar involved in editing classic texts and in spreading Chassidus and seforim in Eretz Yisrael.
Torah scholarship. The Rebbe gave him detailed feedback on halachic sources (IK 510), and critical notes on editions of the Meiri's Beis HaBechirah, insisting on scholarly rigor — transparency about sources, comparison of manuscripts, and careful editing (IK 6761). He also clarified for him fine distinctions in the roles of the Levi'im "in their watches" and "on their platform" (IK 10134).
Chassidus is for every Jew. From the earliest letter, the Rebbe urged him to spread pnimiyus haTorah as essential for the redemption (IK 510). He taught that Chassidus belongs to all Jews in every generation, encouraged spreading it broadly, and wrote about publishing chassidic stories (IK 2455), and urged him to use every opportunity to spread Chassidus in Eretz Yisrael (IK 7913).
Schools and seforim. The Rebbe encouraged him to visit schools, with sensitivity toward students and staff, to distribute seforim, and offered suggestions for book sales (IK 8036). He stressed that order and timely communication are essential for blessing and for effective work (IK 8022), and encouraged detailed letters about spiritual matters (IK 7913).
Inspiration into action. After a visit to Kfar Chabad, the Rebbe wrote that inspiration must lead to practical mitzvah observance (IK 10162). In a later letter he wrote that a true shepherd continues to care for his flock even after his passing (IK 10192).
Sources: the Rebbe's letters cited above.