  We derive the relation between the scattering phase shift and the
two-particle energy in the finite box, which is relevant for extracting the
strong phase shifts in lattice QCD. We consider elastic scattering of two
particles with different mass and with non-zero total momentum in the lattice
frame. This is a generalization of the Luscher formula, which considers zero
total momentum, and the generalization of Rummukainen-Gottlieb's formula, which
considers degenerate particles with non-zero total momentum. We focus on the
most relevant total momenta in practice, i.e. P=(2\pi/L) e_z and P=(2\pi/L)
(e_x+e_y) including their multiples and permutations. We find that the P-wave
phase shift can be reliably extracted from the two-particle energy if the phase
shifts for l>=2 can be neglected, and we present the corresponding relations.
The reliable extraction of S-wave phase shift is much more challenging since
delta(l=0) is always accompanied by delta(l=1) in the phase shift relations,
and we propose strategies for estimating delta(l=0). We also propose the
quark-antiquark and meson-meson interpolators that transform according the
considered irreducible representations.
