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Using $(1310.6\ifmmode\pm\else\textpm\fi{}7.0)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $J/\ensuremath{\psi}$ events acquired with the BESIII detector at the BEPCII storage rings, the decay ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ is observed for the first time with a significance of $8\ensuremath{\sigma}$ via the process $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}^{\ensuremath{'}}$. We measure the branching fraction of ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ to be $\mathcal{B}({\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})=\phantom{\rule{0ex}{0ex}}(1.97\ifmmode\pm\else\textpm\fi{}0.33(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.19(\mathrm{syst}))\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, where the first and second uncertainties are statistical …