On Shabbos, Aug. 17, 1991 (7th of Elul, 5751) during the farbrengen, the Rebbe explained the significance of the head of the generation.
The Rebbe clearly explained the relationship of the head of the genration vis-à-vis other Jews. From other addresses of the Rebbe we know that the head of the generation is the Rebbe himself, it would then follow that Moshe Rabbeinu equals the head of the generation which in turn means the Rebbe.
Here’s what the Rebbe said –
“ He, the leader of the generation is the tzaddik of the generation and is the foundation of Creation, as it says in Proverbs 10:25 “…but the righteous stand firm forever.”
The Tzaddik is the Foundation Stone ( which was the basis of the Temple) and is present in the physical world without any changes including after the burial as opposed to the Ark of the Covenant which was buried (Tractate Yoma54b). He is the judge and prophet present in every generation as a manifestation of a constant Divine force that’s the foundation of the entire existence.
I.e. his existence is evidence of the fact that the world exists and if we were to suppose that the tzaddik is gone, even for a split second, the world could not continue to exist. From this it follows that even after 3 Tammuz, the Rebbe continues his influence even though we can’t see the Rebbe currently. The analogy with the Foundation Stone is telling in the sense that just like it is hidden yet we know that it’s present on the Temple grounds, the same would apply to the Rebbe.
The only other possibility capable of negating the aforementioned would be the presence of another head of the generation but as the Rebbe mentioned many times, beginning in 1951 and numerous times after that, that this generation is the last generation of exile and the first generation of Redemption. And this generation obviously includes the Rebbe himself!