We illustrate how form-invariance transformations can be used for constructing phantom cosmologies from standard scalar field universes. First we discuss how to relate two flat Friedmann-Robertson-Walker cosmologies with different barotropic indexes gamma and gamma;. Then we consider the particular case gamma;=-gamma, and we show that, if the matter content is interpreted in terms of self-interacting scalar fields, then the corresponding transformation provides the link between a standard and a phantom cosmology. After that, we illustrate the method by considering models with exponential potentials. Finally, we also show that the mentioned duality persists even if the typical brane-world modifications to the Friedmann equation are considered.