fbNFR == worth a Queen.
Under the general principle that any piece combining the powers of the Rook (or something worth as much as a Rook) with those of a minor piece (a Knight or Bishop, or anything of roughly equal value) produces a piece worth as much as a Queen, well,fbNFR == worth a Queen.
The Fibnif is worth a piece, so adding a Rook to it should make a new Queen. Although this is probably a weak Queen (it might be a third of a Pawn weaker than the FIDE Queen), picture a position with a White fbNFR on e6 and a Black King on e8.
Gosh, that's checkmate! In fact, fbNFR can force mate without help of its own King.