  The conformal transformation of the Hawking-Hayward quasi-local mass is
reexamined. It has been found recently that the conformal transformation of the
latter exhibits the 'wrong' conformal factor compared to the way usual masses
transform under conformal transformations of spacetime. We show, in analogy
with what was found recently for the Misner-Sharp mass, that unlike the purely
geometric definition of the Hawking-Hayward mass, the latter exhibits the
'right' conformal factor whenever expressed in terms of its material content
via the field equations. The case of conformally invariant scalar-tensor
theories of gravity is also examined. The equivalence between the Misner-Sharp
mass and the Hawking-Hayward mass for spherically symmetric spacetimes
manifests itself by giving identical peculiar behaviors under conformal
transformations.
