That is not my understanding.
Satan is a fallen angel (Michael).
The name Lucifer is used once in the KJ Bible. Lucifer was the human King of Babel. Perhaps his quest to build a tower to heaven was inspired by Satan, but he was not Satan himself.
We both damn well know who Alinsky dedicated his book to and it was no king on earth...
St. Michael the Archangel, defend us in battle. Be our defense against the wickedness and snares of the Devil. May God rebuke him, we humbly pray, and do thou, O Prince of the heavenly hosts, by the power of God, thrust into hell Satan, and all the evil spirits, who prowl about the world seeking the ruin of souls. Amen..