Determine from the balanced chemical reaction if
the derived mole ratio is correct or incorrect.

It's incorrect. There are 6 moles of NaBr produced for every 3 moles of Na₂S among the reactants (as well as 2 moles of FeBr₃), so the mole ratio of NaBr to Na₂S should be 2 : 1, not 1 : 1.