  The $D^+_s\to K^+K^-\mu^+\nu_\mu$ 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 ${\mathcal B}(D^+_s\to \phi \mu^+\nu_\mu) = (2.25\pm 0.09 \pm
0.07) \times10^{-2}$, the most precise measurement to date. Combining with the
world average of ${\mathcal B}(D^+_s\to \phi e^+\nu_e)$, the ratio of the
branching fractions obtained is$\frac{{\mathcal B}(D^+_s\to \phi
\mu^+\nu_\mu)}{{\mathcal B}(D^+_s\to \phi e^+\nu_e)} = 0.94\pm0.08$, in
agreement with lepton universality. By performing a partial wave analysis, the
hadronic form factor ratios at $q^{2}=0$ are extracted, finding
$r_{V}=\frac{V(0)}{A_{1}(0)}=1.58\pm0.17\pm0.02$ and
$r_{2}=\frac{A_{2}(0)}{A_{1}(0)}=0.71\pm0.14\pm0.02$, where the first
uncertainties are statistical and the second are systematic. No significant
$S$-wave contribution from $f_0(980)\to K^+K^-$ is found. The upper limit
$\mathcal{B}(D_s^+\to f_0(980)\mu^{+}{\nu}_{\mu}) \cdot{\mathcal B}(f_0(980)\to
K^+K^-) < 5.45 \times 10^{-4}$ is set at 90\% confidence level.
