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In a companion paper we introduced the notion of asymptotically Minkowski
spacetimes. These space-times are asymptotically flat at both null and spatial
infinity, and furthermore there is a harmonious matching of limits of certain
fields as one approaches $i^\circ$ in null and space-like directions. These
matching conditions are quite weak but suffice to reduce the asymptotic
symmetry group to a Poincar\'e group $\mathfrak{p}_{i^\circ}$. Restriction of
$\mathfrak{p}_{i^\circ}$ to future null infinity $\mathscr{I}^{+}$ yields the
canonical Poincar\'e subgroup $\mathfrak{p}^{\rm bms}_{i^\circ}$ of the BMS
group $\mathfrak{B}$ selected in the companion paper and its restriction to
spatial infinity $i^\circ$ gives the canonical subgroup $\mathfrak{p}^{\rm
spi}_{i^\circ}$ of the Spi group $\mathfrak{S}$ there. As a result, one can
meaningfully compare angular momentum that has been defined at $i^\circ$ using
$\mathfrak{p}^{\rm spi}_{i^\circ}$ with that defined on $\mathscr{I}^{+}$ using
$\mathfrak{p}^{\rm bms}_{i^\circ}$. We show that the angular momentum charge at
$i^\circ$ equals the sum of the angular momentum charge at any 2-sphere
cross-section $S$ of $\mathscr{I}^{+}$ and the total flux of angular momentum
radiated across the portion of $\mathscr{I}^{+}$ to the past of $S$. In general
the balance law holds only when angular momentum refers to ${\rm SO(3)}$
subgroups of the Poincar\'e group $\mathfrak{p}_{i^\circ}$.