  In a Hamiltonian Lie algebroid over a pre-symplectic manifold and over a
Poisson manifold, we introduce a map corresponding to a comomentum map, called
a comomentum section. We show that the comomentum section gives a Lie algebroid
morphism among Lie algebroids. Moreover, we prove that a momentum section on a
Hamiltonian Lie algebroid is a Poisson map between proper Poisson manifolds,
which is a generalization that a momentum map is a Poisson map between the
symplectic manifold to dual of the Lie algebra. Finally, a momentum section is
reinterpreted as a Dirac morphism on Dirac structures.
