Hard to say what your question and what your problem is.
You can use molar conductivity to calculate conductivity of a solution of a known molarity.
Technically speaking it doesn't change with the concentration. In concentrated solutions ions start to interact (for example they create electrically neutral ion pairs) and we can't assume they move independently. This can be understood as if the concentration of freely roaming ions was lower than the actual concentration, so in effect the measured conductivity is lower than expected. That's why we typically report molar conductivity extrapolated to the infinite dilution.