  We investigate the morphological properties of 494 galaxies selected from the
GMASS survey at z>1, primarily in their optical rest frame, using HST images,
from the CANDELS survey. We propose that the Hubble sequence of galaxy
morphologies takes shape at redshift 2.5<z<3. The fractions of both ellipticals
and disks decrease with increasing lookback time at z>1, such that at redshifts
z=2.5-2.7 and above, the Hubble types cannot be identified, and most galaxies
are classified as irregular. The quantitative morphological analysis shows
that, at 1<z<3, morphological parameters are not as effective in distinguishing
the different morphological Hubble types as they are at low redshift. No
significant morphological k-correction was found to be required for the Hubble
type classification, with some exceptions. In general, different morphological
types occupy the two peaks of the rest-frame (U-B) colour bimodality of
galaxies: most irregulars occupy the blue peak, while ellipticals are mainly
found in the red peak, though with some level of contamination. Disks are more
evenly distributed than either irregulars and ellipticals. We find that the
position of a galaxy in a UVJ diagram is related to its morphological type: the
"quiescent" region of the plot is mainly occupied by ellipticals and, to a
lesser extent, by disks. We find that only ~33% of all morphological
ellipticals in our sample are red and passively evolving galaxies. Blue
galaxies morphologically classified as ellipticals show a remarkable structural
similarity to red ones. Almost all irregulars have a star-forming galaxy
spectrum. In addition, the majority of disks show some sign of star-formation
activity in their spectra, though in some cases their red continuum is
indicative of old stellar populations. Finally, an elliptical morphology may be
associated with either passively evolving or strongly star-forming galaxies.
