Some insights on bicategories of fractions - III

We fix any bicategory $\mathcal{A}$ together with a class of morphisms ${\mathbf{W}}_{\mathcal{A}}$, such that there is a bicategory of fractions $\mathcal{A}[{\mathbf{W}}_{\mathcal{A}}^{-1}]$. Given another such pair $(\mathcal{B},{\mathbf{W}}_{\mathcal{B}})$ and any pseudofunctor $\mathcal{F}:\mathcal{A}\to \mathcal{B}$, we find necessary and sufficient conditions in order to have an induced equivalence of bicategories from $\mathcal{A}[{\mathbf{W}}_{\mathcal{A}}^{-1}]$ to $\mathcal{B}[{\mathbf{W}}_{\mathcal{B}}^{-1}]$. In particular, this gives necessary and sufficient conditions in order to have an equivalence from any bicategory of fractions $\mathcal{A}[{\mathbf{W}}_{\mathcal{A}}^{-1}]$ to any given bicategory $\mathcal{B}$.