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 equivalence of bicategories from $mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]$ to $mathscr{B}[mathbf{W}_{mathscr{B}}^{-1}]$. In particular, this gives necessary and sufficient conditions in order to have an equivalence from any bicategory of fractions $mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]$ to any given bicategory $mathscr{B}$.
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