There is no such thing as a "fake" Shikai or Bankai it was just incomplete. Ichigo’s original Shikai was always the true Zangetsu, just not in its proper form. Per Kubo’s Q&A 357, a true Zanpakuto consists of a blade and a scabbard. For Ichigo, his dual Shikai represents both parts (large blade = scabbard, small blade = core blade)
When he goes Bankai, they fuse into a single weapon where the outer white shell is the scabbard and the inner black sword is the blade. When Yhwach broke the outer white shell, it revealed the core blade underneath (which resembled his original Shikai). Because Ichigo absorbed the broken scabbard back into his body, he can now freely switch between wielding the dual blades or the single blade.