  The decay-time-dependent $CP$ asymmetry in $B^0_s\to J/\psi(\to
\mu^{+}\mu^{-}) K^{+}K^{-}$ decays is measured using proton-proton collision
data, corresponding to an integrated luminosity of 6 $fb^{-1}$, collected with
the LHCb detector at a center-of-mass energy of 13 TeV. Using a sample of
approximately 349 000 $B^{0}_{s}$ signal decays with an invariant $K^{+}K^{-}$
mass in the vicinity of the $\phi(1020)$ resonance, the $CP$-violating phase
$\phi_s$ is measured, along with the difference in decay widths of the light
and heavy mass eigenstates of the $B^0_s$-$\bar{B}^0_s$ system,
$\Delta\Gamma_s$, and the difference of the average $B^0_s$ and $B^0$ meson
decay widths, $\Gamma_s-\Gamma_d$. The values obtained are $\phi_s = \ -0.039
\pm 0.022 \pm 0.006$ rad, $\Delta\Gamma_s = 0.0845 \pm 0.0044 \pm 0.0024 $
ps$^{-1}$ and $\Gamma_s-\Gamma_d = -0.0056 ^{+ 0.0013}_{-0.0015} \pm 0.0014$
ps$^{-1}$, where the first uncertainty is statistical and the second
systematic. These are the most precise single measurements to date and are
consistent with expectations based on the Standard Model and with the previous
LHCb analyses of this decay. These results are combined with previous
independent LHCb measurements. The phase $\phi_s$ is also measured
independently for each polarization state of the $K^{+}K^{-}$ system and shows
no evidence for polarization dependence.
