[SunkenCiv]

Amenhotep III did take an interest in the Giza monuments, as the other pharaohs of the later 18th dynasty. But the head was obviously recarved (out of scale, much better preserved than the body), and the most likely match would be from the 25th (Kushite) dynasty.

[PIF]

Amenhotep II of the 12th Dynasty, not III, sorry. Very close match and right head dress for the period. The 25th did not use that head dress.

See "The Sphinx Mystery" by R Temple, pp. 187-195, figures 4.29 & 4.30 (Sphinx A23).