  The positive mass theorem states that the total mass of a complete
asymptotically flat manifold with non-negative scalar curvature is
non-negative; moreover, the total mass equals zero if and only if the manifold
is isometric to the Euclidean space. Huang and Lee [2015] proved the stability
of the Positive Mass Theorem for a class of $n$-dimensional ($n \geq 3$)
asymptotically flat graphs with non-negative scalar curvature, in the sense of
currents. Motivated by their work and using results of Dahl, Gicquaud and
Sakovich [2013], we adapt their ideas to obtain a similar result regarding the
stability of the positive mass theorem, in the sense of currents, for a class
of $n$-dimensional $(n \geq 3)$ asymptotically hyperbolic graphs with scalar
curvature bigger than or equal to $-n(n-1)$.
