The balanced molecular equation for the reaction is:
\[
\boxed{\mathrm{Ni}_{2}\left(\mathrm{SO}_{3}\right)_{3}(aq) + 2\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4}(aq) \rightarrow 2\mathrm{NiPO}_{4}(s) + 3\mathrm{(NH}_{4})_{2}\mathrm{SO}_{3}(aq)}
\]