  In the exceptional field theory, there are two natural parameterizations for
the generalized metric; in terms of bosonic fields in the eleven-dimensional
supergravity (M-theory parameterization) and the type IIB supergravity (type
IIB parameterization). In order to translate various results known in the
M-theory to the type IIB theory or vice versa, an explicit map between the two
parameterizations will be useful. In this note, we present such a linear map.
Comparing the two parameterizations under the linear map, we reproduce the
known T-duality transformation rules for the supergravity fields. We also
obtain the T-duality rules for non-geometric $\beta$-/$\gamma$-fields appearing
in the type II theory on a torus.
