Did Einstein know that the speed of light is variable? Yes. Banesh Hoffmann, his co-author: Einstein "resisted the temptation" to admit that the Michelson-Morley experiment had DIRECTLY proved variability as per Newton, and took from the ether "the one aspect that he needed":

Albert Einstein: "I introduced the principle of the constancy of the velocity of light, which I borrowed from H. A. Lorentz's theory of the stationary luminiferous ether." https://en.wikipedia.org/wiki/Lorentz_ether_theory

Banesh Hoffmann, Relativity and Its Roots, p.92: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether. If it was so obvious, though, why did he need to state it as a principle? Because, having taken from the idea of light waves in the ether the one aspect that he needed, he declared early in his paper, to quote his own words, that "the introduction of a 'luminiferous ether' will prove to be superfluous." https://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768

Pentcho Valev https://twitter.com/pentcho_valev

So Einstein "resisted the temptation" to obey the truth (variable speed of light) provided by the Michelson-Morley experiment. Then, in 1921, already a deity, Einstein proclaimed that the experiment had proved constancy of the speed of light. Due to its divine origin, the blatant lie immediately became absolute truth and has been universally taught ever since:

The New York Times, April 19, 1921: "The special relativity arose from the question of whether light had an invariable velocity in free space, he [Einstein] said. The velocity of light could only be measured relative to a body or a co-ordinate system. He sketched a co-ordinate system K to which light had a velocity C. Whether the system was in motion or not was the fundamental principle. This has been developed through the researches of Maxwell and Lorentz, the principle of the constancy of the velocity of light having been based on many of their experiments. But did it hold for only one system? he asked. He gave the example of a street and a vehicle moving on that street. If the velocity of light was C for the street was it also C for the vehicle? If a second co-ordinate system K was introduced, moving with the velocity V, did light have the velocity of C here? When the light traveled the system moved with it, so it would appear that light moved slower and the principle apparently did not hold. Many famous experiments had been made on this point. Michelson showed that relative to the moving co-ordinate system K1, the light traveled with the same velocity as relative to K, which is contrary to the above observation. How could this be reconciled? Professor Einstein asked." https://ebay.com/itm/ALBERT-EINSTEIN-Lecture-on-SPEED-OF-LIGHT-Time-1st-Visit-to-US-1921-Newspaper/373400655156

Pentcho Valev https://twitter.com/pentcho_valev