  The irreducible representations (IRs) of the double cover of the Euclidean
group with parity in three dimensions are subduced to the corresponding cubic
space group. The reduction of these representations gives the mapping of
continuum angular momentum states to the lattice in the case of non-zero linear
momentum. The continuous states correspond to lattice states with the same
momentum and continuum rotational quantum numbers decompose into those of the
IRs of the little group of the momentum vector on the lattice. The inverse
mapping indicates degeneracies that will appear between levels of different
lattice IRs in the continuum limit, recovering the continuum angular momentum
multiplets. An example of this inverse mapping is given for the case of the
``moving'' isotropic harmonic oscillator.
