For reference, here is the complete sentence from page 1 in the paper:
The helicity formalism is well suited to relativistic problems bcause the helicity operator $h=\vec S\cdot\hat p$ is invariant under both rotations and boosts along $\hat p$.
The context suggests that the hat on $\hat p$ is meant to indicate a unit vector. Even if we ignore any statements about helicity, this is already in conflict with any Lorentz boost that transforms the momentum to zero: the zero vector cannot be a unit vector.
This problem goes away if the particle is massless because then its momentum is never zero, and a simple Lorentz boost along $\hat p$ cannot change the sign of $\hat p$. However, I did not see anything in the context that assumes a massless particle. Maybe the author is assuming that "helicity" implies "massless."