Right saturations and induced pseudofunctors between bicategories of fractions

We fix any bicategory A together with a class of morphisms WA, such that there is a bicategory of fractions A[WA−1] (as described by D. Pronk). Given another such pair (B,WB) and any pseudofunctor F:A→B, we find necessary and sufficient conditions in order to have an induced pseudofunctor G:A[WA−1]→B[WB−1]. Moreover, we give a simple description of G in the case when the class WB is “right saturated”.