According to an FBI Memo Released in regards to the JFK assassination, the Soviets had intelligence that Lyndon B. Johnson was behind the killing of JFK.
One passage of the memo notes that Johnson was considered virtually unknown to the Soviet leaders, and that their intelligence agencies suspected his involvement in the assassination:
Our source added that “now” the K.G.B. was in possession of data purporting to indicate President Johnson was responsible for the assassination of the late President John F. Kennedy.
The intelligence, some of which was gathered by a source who was inside Russia when Kennedy was assassinated, details how Communist Party leaders believed the killing was part of an “ultraright” conspiracy to “effect a ‘coup.’” Soviet officials also claimed not to have a connection with Oswald.
Now, this is by no means proof Lyndon B. Johnson was behind it. This could have just been a theory that was picked up during their investigation. With that being said Roger Stone has pointed the finger at Johnson as the man behind the attack and even wrote an entire book about it. More documents would be needed to confirm this.