Chapter 16 of Rabbi Shloma Majeski’s Likkutei Mekoros, Volume 2, responds to the questions: Where does the Rebbe explain why he refers to the Previous Rebbe when he actually means himself? Where does the Rebbe state that he and the Previous Rebbe are one and the same? (Underlined text is the compiler’s emphasis).
14. The Rebbe [Rayatz]’s proclamation, “l’alter l”geula – immediate redemption,” was heavily publicized; everyone knew that the Lubavitcher Rebbe spoke a good deal about Moshiach.
There were once two Jews in a train that passed by the station you get off at to go to the Rebbe’s house. One Jew told the other, “the Lubavitcher Rebbe lives here.” The second Jew asked him, “what are Lubavitchers?” The first Jew answered in earnest: “Lubavitchers are the Jews who believe in Moshiach.”
We have discussed how the main thing is to draw down G-dliness into the physical world. In this vein, there is the story of how one time, in a conversation between the Maggid and the Alter Rebbe, the Maggid mentioned gilui Eliyahu, a G-dly revelation characterized by the presence of the prophet Eliyahu. The Alter Rebbe remarked that he would like to behold this vision. The Maggid told “the Litvak [i.e., the Alter Rebbe] … Moshiach should in fact be experienced overtly, in a way that is visible to the human eye [i.e., gilui Eliyahu, a spiritual vision, is not the ultimate intent]; the advent of Moshiach should take place literally, in the physical sense.”
15. [The Rebbe Shlita delivered a maamer, pausing at times to say l’chaim and sing niggunim, during which time he also spoke to certain individuals. The following exchange took place with one of those people.] Why now do you want it all? … It is the same Rebbe with the same approach, just wearing different clothing, brighter clothing. Why does this bother you? It is the same Rebbe!
(Sichos Kodesh 5713, pg. 126)