Information ratio

Is this statement correct?

Among active portfolios, the portfolio with the highest information ratio will have the highest sharpe ratio.

Do we have to add a condition that they use the same benchmark or we can directly assume that the benchmark sharpe ratio is the same for all similar active portfolios?

well of course, information ratio is not useful/comparable if the ratios are calculated from different benchmarks

information ratio = (Rp - RB)/active risk

different benchmarks= different benchmark return and active risk.