That’s actually wrong. Marx came up with it, he just called what Lenin called “Socialism” as “lower-stage Communism.” The origin is in Historical Materialism, and the concept of Scientific Socialism (as opposed to the Utopian form that thought you could just think up a good society and create it outright).

Calling it a “continuum” is misleading. Capitalism, as an example, starts with many smaller Capitalists but eventually concentrates and monopolizes. This is a trackable and historical motion, not a “continuum” but nonetheless an observed trend. Socialism, on the other hand, continues that movement but does so in the direction of collectivization, as public ownership and planning not only becomes feasible but far more efficient at higher levels of development, which is also observable and trackable.

Communism is when this process has been done and all private property has been folded into the public sector. This isn’t a straight and narrow line, but a process that will happen in many different manners across many different countries, but by tracking trajectories and behaviors this prediction becomes clearer and clearer, and Marx becomes vindicated by the passage of time as we observe them coming to fruition.