The $D_s^{+}\to K^{+}{K}^{-}{\mu }^{+}{\nu }_{\mu }$ $$ {D}_s^{+}\to {K}^{+}{K}^{-}{\mu}^{+}{\nu}_{\mu } $$ decay is studied based on 7.33 fb −1 of e + e − collision data collected with the BESIII detector at center-of-mass energies in the range from 4.128 to 4.226 GeV. The absolute branching fraction is measured as $B\left(D_s^{+}\to \varphi {\mu }^{+}{\nu }_{\mu }\right)=\left(2.25\pm 0.09\pm 0.07\right)\times {10}^{-2}$ $$ \mathcal{B}\left({D}_s^{+}\to \phi {\mu}^{+}{\nu}_{\mu}\right)=\left(2.25\pm 0.09\pm 0.07\right)\times {10}^{-2} $$ , the most precise measurement to date. Combining with the world average of $B\left(D_s^{+}\to \varphi e^{+}{\nu }_e\right)$ $$ \mathcal{B}\left({D}_s^{+}\to \phi {e}^{+}{\nu}_e\right) $$ , the ratio of the branching fractions obtained is $\frac{B\left(D_s^{+}\to \varphi {\mu }^{+}{\nu }_{\mu }\right)}{B\left(D_s^{+}\to \varphi e^{+}{\nu }_e\right)}=0.94\pm 0.08$ $$ \frac{\mathcal{B}\left({D}_s^{+}\to \phi {\mu}^{+}{\nu}_{\mu}\right)}{\mathcal{B}\left({D}_s^{+}\to \phi {e}^{+}{\nu}_e\right)}=0.94\pm 0.08 $$ , in agreement with lepton universality. By performing a partial wave analysis, the hadronic form factor ratios at q 2 = 0 are extracted, finding $r_V=\frac{V\left(0\right)}{A_1\left(0\right)}=1.58\pm 0.17\pm 0.02$ $$ {r}_V=\frac{V(0)}{A_1(0)}=1.58\pm 0.17\pm 0.02 $$ and $r_2=\frac{A_2\left(0\right)}{A_1\left(0\right)}=0.71\pm 0.14\pm 0.02$ $$ {r}_2=\frac{A_2(0)}{A_1(0)}=0.71\pm 0.14\pm 0.02 $$ , where the first uncertainties are statistical and the second are systematic. No significant S-wave contribution from f 0(980) → K + K − is found. The upper limit $B\left(D_s^{+}\to f_0\left(980\right){\mu }^{+}{\nu }_{\mu }\right)\cdot B\left(f_0\left(980\right)\to K^{+}{K}^{-}\right)<5.45\times {10}^{-4}$ $$ \mathcal{B}\left({D}_s^{+}\to {f}_0(980){\mu}^{+}{\nu}_{\mu}\right)\cdot \mathcal{B}\left({f}_0(980)\to {K}^{+}{K}^{-}\right)<5.45\times {10}^{-4} $$ is set at 90% credibility level.