T-duality off shell in 3D Type II superspace

We give the manifestly T-dual formulation of the massless sector of the classical 3D Type II superstring in off-shell 3D $N\,=\,2$ superspace, including the action. It has a simple relation to the known superspace of 4D $N\,=\,1$ supergravity in 4D M-theory via 5D F-theory. The prepotential appears as part of the vielbein, without derivatives.