  We report accurate molecular dynamics calculations of the shear stress
relaxation in a two-dimensional strongly coupled Yukawa liquid over a wide
range of the Coulomb coupling strength $\Gamma$ and the Debye screening
parameter $\kappa$. Our data on the relaxation times of the ideal- , excess-
and total shear stress auto-correlation ($\tau^{id}_M, \tau^{ex}_M, \tau_M$
respectively) along with the lifetime of local atomic connectivity $\tau_{LC}$
leads us to the following important observation. Below a certain crossover
$\Gamma_c(\kappa)$, $\tau_{LC} \rightarrow \tau^{ex}_M$, directly implying that
here $\tau_{LC}$ is the microscopic origin of the relaxation of excess shear
stress unlike the case for ordinary liquids where it is the origin of the
relaxation of the total shear stress. At $\Gamma >> \Gamma_c(\kappa)$ i.e. in
the potential energy dominated regime, $\tau^{ex}_M\rightarrow \tau_M$ meaning
that $\tau^{ex}_M$ can fully account for the elastic or "solid like" behavior.
