  We consider the 3D incompressible Hall-MHD system and prove a stability
theorem for global large solutions under a suitable integrable hypothesis in
which one of the parcels is linked to the Hall term. As a byproduct, a class of
global strong solutions is obtained with large velocities and small initial
magnetic fields. Moreover, we prove the local-in-time well-posedness of
$H^{2}$-strong solutions which improves previous regularity conditions on
initial data.
