  The study of the symmetry of Pais-Uhlenbeck oscillator initiated in [Nucl.
Phys. B 885 (2014) 150] is continued with special emphasis put on the
Hamiltonian formalism. The symmetry generators within the original Pais and
Uhlenbeck Hamiltonian approach as well as the canonical transformation to the
Ostrogradski Hamiltonian framework are derived. The resulting algebra of
generators appears to be the central extension of the one obtained on the
Lagrangian level; in particular, in the case of odd frequencies one obtains the
centrally extended l-conformal Newton-Hooke algebra. In this important case the
canonical transformation to an alternative Hamiltonian formalism (related to
the free higher derivatives theory) is constructed. It is shown that all
generators can be expressed in terms of the ones for the free theory and the
result agrees with that obtained by the orbit method.
