According to Einstein, electron absorbs complete energy of photon but due
to its interaction with the atoms of material some energy is lost.
So, In photoelectric experiment the ejected electrons have a wide range of kinetic energy even if the photons striking the surface have same energy. This is true.
But the statement 'According to Einstein, electrons can absorb any fraction of the energy of the striking photon' is not correct. Because the electron can absorb the energy integral multiple of hν.