How to relate the conductance of an aqueous electrolyte to its conductivity
The answer is quite simple, if you look at the equation carefully. Conductance and conductivity are related by cell constant, $\displaystyle\frac{\text{Area}}{\text{Distance}},$ where the area is the area of the electrodes and the distance is the distance between the electrodes.
$$G = \sigma\frac{A}{l}$$
In conductivity measurements, the cell constant was either given by the manufacturer or it was determined experimentally by making a certain concentration of $\ce{KCl}$, the conductivity of which was well established and standardized.
In short, you cannot convert micromho to conductivity because you do not know the cell constant. And weight by weight conversion to molarity is not that trivial. You need to know exact density of each solution.
Did you see the end pages of the manual from you posted the old graph, there is a useful chart (for future readers).