  It is known that the topological T-duality exchanges $H$ and $F$-fluxes. In
this paper, we reformulate the topological T-duality as an exchange of two Lie
algebroids in the generalized tangent bundle. Then, we apply the same
formulation to the Poisson-generalized geometry, which is introduced in
arXiv:1408.2649 to define $R$-fluxes as field strength associated with
$\beta$-transformations. We propose a definition of $Q$-flux associated with
$\beta$-diffeomorphisms, and show that the topological T-duality exchanges $R$
and $Q$-fluxes.
