It’s Trotskyist propaganda. Stalin and Lenin had been allies since they first met in 1905 whereas Trotsky hadn’t even joined the party until 1917, between the two revolutions. Before then, Lenin had frequently called him a traitor and semi-Menshevik. Lenin’s testament, which was written in late 1922 and early 1923 after Lenin had had multiple strokes, included criticism of all the most prominent party members, including Trotsky. Stalin had been elected head of the party in 1921, before Lenin’s first stroke.

In terms of their policies, Lenin and Stalin were both part of the main Bolshevik group, between the ultra-left Trotskyists and rightist Bukharinists. Bukharin had been an ultra-leftist during the civil war but moved to the right during the 1920s. Trotskyists believed the revolution could only succeed if it spread to the most industrialized countries and wanted rapid collectivization. They saw the proletariat as the only revolutionary class and rejected the peasantry. Bukharin strongly supported the NEP and wanted it to continue instead of collectivizing. He believed that even the kulaks (bourgeois farm owners) could lead to socialism. The Trotskyists opposed the self-determination of nations and thought it was a nationalist deviation, while the majority of the party supported it.

If you want more information, Ludo Martens’ book Another View of Stalin has a section on this.

nope, people say that they gling to a letter wrote at the end of lenins life, where he complains stalin being rude to nadjeda krupskaia, iirc this was also used in the nikita khrushchev secret speech

The TLDR version of this history;

Lenin and Stalin were colleagues, and there's not much that actually supports any sort of "beef". The thing that's usually used is this letter, wherein Lenin complains about Stalin. There is reason to believe that the letter is faked by devious actors, but even if it is real, it just reads as venting. Taking "Lenin hated Stalin!" from the letter is like assuming best friends secretly hate each other because one of them made a post while upset on social media.

Stalin was a staunch supporter of Leninism, and stayed true to Lenin's ideals of the Soviet Union while expanding the theory to fit the geopolitical situations that unfolded under Stalin's time as chairman. Foundations of Leninism is a summary of Leninism written by Stalin himself, who wasn't much of a writer.

The whole thing seems to be propaganda by Trots and Anti-Communists to pose Stalin as an evil dictator who illegally took power of the Soviet Union for his own benefit, against the will of Lenin. But the reality is Stalin was democratically elected into this position and staunchly upheld Marxism-Leninism and led projects that benefitted the entire Union and her people. Stalin is a beloved figure by not just Russians and Communists in the western-sphere, but by people in every corner of the world for good reason.

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No but the soviet upper rank did have a bias against Lenin and saught to censor Lenins criticisms of Stalin by means of not delivering Lenins letters to parliment criticizing Stalin and warning against a cult of personality.

Lenin was bed bound and unable to leave care in the last year of his life, he spent it writing letters to parliment, most of which where 'lost' or not delivered, or censored by people looking to please Stalin, unknowingly to Stalin.

Id reccomend reading Lenins letters in the final year of his life, they are avilable.

Edit: Source https://www.marxists.org/history/etol/newspape/ni/vol02/no01/lenin.htm