  We establish a gluing theorem for linearised vacuum gravitational fields in
Bondi gauge on a class of characteristic surfaces in static vacuum
four-dimensional backgrounds with cosmological constant $\Lambda \in
\mathbb{R}$ and arbitrary topology of the compact cross-sections of the null
hypersurface. This generalises and complements, in the linearised case, the
pioneering analysis of Aretakis, Czimek and Rodnianski, carried-out on
light-cones in Minkowski spacetime.
