As far as playing out why Monitors call humans reclaimers (remember it was Primordium that "made" humans reclaimers of the mantle "through long study", not the forerunners...initially). I believe a small part of the book-very small-will mention something along the lines of the Didact telling the Council that they ultimately paid their price in the hands of the Preursors/Prim/Flood, accepted their defeat and programming their monitors and installations with the...idea?...that humans are forerunners (Child of my makers...) as like an act of reconciliation. Afterwards, banishing themselves from the galaxy (or died from the halo array). closer to the end i'm sure.
regardless there has to be an explanation why Forerunners/FR Monitors and not the Precursors named, whether forced or not, Humanity reclaimers.
ps I know the Primordium named humans reclaimers. but what made FR call them as well?
idk.