How could he do that? By legal agreement, all songs either one of them wrote were credited to both until they dissolved the agreement after the Beatles broke up. I looked it up, and it's still credited to both, even though everyone knows one wrote it.
All I know is I read an article on the subject of his changing the authorship many moons ago. He probably had documented proof and it wasn’t contested by Lennon’s lawyers.
Precisely correct. Everything was Lennon-McCartney.