My understanding is that even up to that point, Paul or John, would bring in a nearly completed song idea for the band to complete, and after that it became a PURELY separate endeavor.
However, none of this is to minimize the various small, but essential tweaks contributed by the band itself during the recording sessions, including Fifth Beatle, producer George Martin.
Whatever the case may be, the Lennon-McCartney synergy was ruined by their fame, IMHO. This group stopped being amazing after about a year of worldwide adulation. For John and Paul, the stress took its toll on their relationship and each started thinking he could do it all, and without as much effort. Hope I don’t sound too harsh.