This is a Video by Finnish Bolshevik with Stephen Kotkin the right-wing historian who specializes on the Stalin period speaking on the video.
Finnish Bolshevik says he does not agree with Stephen Kotkin views, Kotkin is a conservative and a pretty classical anti-communist.
However some of his research, especially regarding primary source documents is interesting.
Its worth pointing out that the idea that the "Testament" of Lenin was a forgery was not invented by Kotkin.
Many marxists also believed this to be the case
The Forgery of the 'Lenin Testament'
... Some have also alleged that Lenin did dictate the document but had lost his senses due to illness.
This was the opinion of Lenin's sister Maria Ulyanova.
However this might be a convenient cover for her mother Krupskaya. Krupskaya had to have known about the forgery if it took place.
However she became a support of Stalin's despite her earlier support for Zinoviev.
Therefore this explanation could have been most convenient for all in the Stalin-team.
The charge leveled against Stalin in the "testament" is not one about politics, but about "rudeness".
The bizarre nature of the charge contributed to the idea that it was not written by Lenin at all, or at least not when in full possession of his faculties.
Stalin himself never publicly discussed the authenticity of the "testament", instead he apologized and accepted the charge of "rudeness" but turned it into a weapon against his opponents, saying he can't help being rude to those who harm the Bolshevik party.
Lenin's "testament" is mostly brought up by Trotskyists.
In deed the term was invented by them.
However when hearing about most people think Lenin allegedly wanting to choose a successor is very anti-Lenin, anti-Bolshevik thing to do.
It goes against his character to do such a thing.
Lenin would have respected the party's vote, and certainly wouldn't have let personal issues or "rudeness" intervene with politics.
In the 1930s Trotsky claimed Lenin allegedly named him his successor in his "testament".
However in 1925 Trotsky said:
"Lenin has not left any “Testament”; the character of his relations to the party, and the character of the party itself, preclude the possibility of such a “Testament.” ~Trotsky,
Letter on Eastman's book Trotsky could have been pressured into saying this, as anything else would have resulted in merciless ridicule by rival politicians.
But its also possible Trotsky simply had more honesty and guts in 1925 then in his later years.
Finnish Bolshevik thoughts on the alleged forgery