  We show that the asymptotic charges associated with Lorentz symmetries on
past and future null infinity match in the limit to spatial infinity in a class
of asymptotically-flat spacetimes. These are spacetimes that obey the
Ashtekar-Hansen definition of asymptotic flatness at null and spatial infinity
and satisfy an additional set of conditions which we lay out explicitly.
Combined with earlier results on the matching of supertranslation charges, this
shows that all Bondi-Metzner-Sachs (BMS) charges on past and future null
infinity match in the limit to spatial infinity in this class of spacetimes,
proving a relationship that was conjectured by Strominger. Assuming additional
suitable conditions are satisfied at timelike infinities, this proves that the
flux of all BMS charges is conserved in any classical gravitational scattering
process in these spacetimes.
