Did Vladimir Lenin send Mussolini a congratulatory telegram when Mussolini successfully marched on Rome in 1922?
I checked Lenin's "Collected Works," Volume 33, 1921-1923. There is nothing even close to such a telegram. (For comparison, the volume contains such "masterpieces" as a letter to a Congress of Statisticians, from November 4, 1922, consisting of a single sentence.) Hence, it is very unlikely that this telegram ever existed.
This volume of "Collected Works" contains only few items where Italy is mentioned. The only place fascists are mentioned, is in the passage on page 141 (a speech at Comintern on November 13, 1922):
The fascists in Italy may, for example, render us a great service by showing the Italians that they are not yet sufficiently enlightened and that their country is not yet ensured against the Black Hundreds. Perhaps this will be very useful.
This is just few weeks after "March on Rome" and is clearly not meant to be a congratulation. But maybe somebody mistook it for one...
Lastly, if you want to dig even deeper in this cesspool (and if you can read Italian), consider reading the book
"Mussolini contro Lenin" by Emilio Gentile, 2017.
I did not read the book myself (and I am not planning to), but a review of the book states:
Gentile writes that the Russian press did not publish anything on the coming to power of the former socialist and revolutionary Mussolini. The [fascist] newspaper "Popolo d'Italia" published a brief chronicle of the events in Moscow on November 29, 1922 under the heading “Moscow's Displeasure. Communist mourning of Mussolini taking power" (p. 219 of Gentile's book).
See for instance here if you are unfamiliar with this organization.
Edit. Given the well-established history of Soviet authorities rewriting repeatedly the history of the (former) USSR, it is not impossible, that some materials were removed from Lenin's archives or not included in the "Collected Works." But, in this particular case, the existence of a claimed congratulatory telegram would go against of what is known. Hence, in this particular case, I am willing to trust the official publication. I remember (just do not ask me to find the precise reference and do not ask me why was I reading this staff) two instances in collected works of Lenin, resp. Stalin (the latter published in his collected works when the latter was still alive) where the published pieces did not fit the official narrative. In one case (Lenin), written around 1919, he was praising some emerging German movement combining "socialism and nationalism." (I have a good guess what this movement later became.) In the other case (Stalin's), it was an opinion piece published in Spring of 1917 in "Pravda" which was supportive of the Provisional Government (this was against proposed Lenin's policy at the time). That piece was accompanied by a later added explanation that such a disagreement was not a problem, nothing to see here.