NP-completeness of minimal queen completion on chessboards

Let $n$ be a positive integer and let $Q$ be a set of $k$ queens placed on an $n\times n$ chessboard. For a nonnegative integer $l$, the minimal chessboard domination queen completion problem asks whether there is a set $Q'$ of size $k+l$ such that $Q\subset Q'$ and $Q'$ dominates the chessboard.

Chessboard queen completion conjecture. The minimal chessboard domination queen completion problem is NP-complete.

The problem concerns completing a prescribed partial queen placement to a dominating placement with a specified increase in size. The paper presents the claim as an open conjecture and does not provide a proof of NP-completeness.