  Observations have shown that the star-formation activity and the morphology
of galaxies are closely related, but the underlying physical connection is not
well understood. Using the TNG50 simulation, we explore the quenching and the
morphological evolution of the 102 massive quiescent galaxies in the mass range
of $10.5<\log(M_{\rm stellar}/M_{\odot})<11.5$ selected at $z=0$. The
morphology of galaxies is quantified based on their kinematics, and we measure
the quenching timescale of individual galaxies directly from star formation
history. We show that galaxies tend to be quenched more rapidly if they: (i)
are satellites in massive halos, (ii) have lower star-forming gas fractions, or
(iii) inject a larger amount of black hole kinetic feedback energy. By
following the global evolutionary pathways, we conclude that quiescent discs
are mainly disc galaxies that are recently and slowly quenched. Approximately
half of the quiescent ellipticals at $z=0$ are rapidly quenched at higher
redshifts while still disc-like. While being quiescent, they gradually become
more elliptical mostly by disc heating, yet these ellipticals still retain some
degree of rotation. The other half of quiescent ellipticals with the most
random motion-dominated kinematics build up large spheroidal components before
quenching primarily by mergers, or in some cases, misaligned gas accretion.
However, the mergers that contribute to morphological transformation do not
immediately quench galaxies in many cases. In summary, we find that quenching
and morphological transformation are decoupled. We conclude that the TNG black
hole feedback -- in combination with the stochastic merger history of galaxies
-- leads to a large diversity of quenching timescales and a rich morphological
landscape.
