  This note gives a concise derivation of a twistor-initial-data
characterisation of pp-wave spacetimes in vacuum. The construction is based on
a similar calculation for the Minkowski spacetime in [Class. Quantum Grav. 28
075010]. The key difference is that for the Minkowski spacetime a necessary
condition is that $\nabla_{A}{}^{A'}\bar{\kappa}_{A'} \neq 0$. In this note it
is shown that if $\nabla_{A}{}^{A'}\bar{\kappa}_{A'}=0$ then the development is
a pp-wave spacetime. Furthermore, it is shown that such condition propagates
off the initial hypersurface, which, in turn, gives a twistor initial data
characterisation of pp-waves.
