According to Wikipedia, Williams re-recorded the fanfare for Empire Strikes Back and his version was used in the subsequent Lucas-helmed Star Wars movies.
https://en.wikipedia.org/wiki/20th_Century_Fox
Incidentally, it seems that the “slanted 0” 20th Century Fox logo originally designated Cinemascope as well. Do we know why that particular version of the logo was used in Empire Strikes Back but not SW or ROTJ?