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In this talk we will construct via Daniel's sister correspondence in \(\mathbb{H}^2\times\mathbb{R}\) a \(2\)-parameter family of Alexandrov-embedded constant mean curvature \(0\,\)<\(\,H\leq 1/2\) surfaces in \(\mathbb{H}^2\times \mathbb{R}\) with \(2\) ends and genus \(0\). They are symmetric with respect to a horizontal slice and \(k\) vertical planes disposed symmetrically. We will discuss the embeddedness of the constant mean curvature surfaces of this family, and we will show that the Krust property does not hold for \(0\,\)<\(\,H\leq 1/2\); i.e, there are minimal graphs over convex domain in \(\widetilde{\text{SL}}_2(\mathbb{R})\) and \(\text {Nil}_3\) whose sister conjugate surface is not a vertical graph in \(\mathbb{H}^2\times\mathbb{R}\).