We fix any bicategory $mathscr{A}$ together with a class of morphisms $mathbf{W}_{mathscr{A}}$, such that there is a bicategory of fractions $mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]$. Given another such pair $(mathscr{B},mathbf{W}_{mathscr{B}})$ and any pseudofunctor $mathcal{F}:mathscr{A}rightarrowmathscr{B}$, we find necessary and sufficient conditions in order to have an induced pseudofunctor $mathcal{G}:mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]rightarrow mathscr{B}[mathbf{W}_{mathscr{B}}^{-1}]$. Moreover, we give a simple description of $mathcal{G}$ in the case when the class $mathbf{W}_{mathscr{B}}$ is right saturated.
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