The solution is already infinitely dilute, meaning the molar conductivity is at its maximum value. Adding more water will not dilute the solution further; therefore, there will be no change in molar conductivity. It will remain the same.
\[\text{Molar conductivity } (\Lambda_m) \propto \frac{\kappa}{c}\]
where $\kappa$ is the conductivity and $c$ is the concentration. For infinitely dilute solutions, $c$ is already approaching zero, and $\Lambda_m$ becomes constant.