  In this paper, we establish graded T-duality for $2d$ $\sigma$-models with
$H$-flux after localization. This establishes the most general version of
T-duality for Type II String Theory. The graded T-duality map, which we call
{\bf graded Hori morphism}, is compatible with the Jacobi property of the
graded fields, that was earlier studied in \cite{HM21}. Also included are some
open problems/conjectures.
