  We analize the entanglement change, under a Lorentz transformation, of a
system consisting of two spin-one particles, considering different partitions
of the Hilbert space, which has spin and momentum degrees of freedom. We show
that there exists a complete set of states of the spin subspace in which the
entanglement change of any state in the set is zero for all partitions and all
values of the Wigner angle. Moreover, these states only change by a global
phase factor under the Lorentz boost. Within this basis, maximally entangled
invariant states, interesting for quantum information purposes, are explicitly
obtained. On the other hand, the entanglement in the particle- particle
partition is Lorentz invariant, thus protecting the consistency of quantum
correlations and teleportation results. We show how our results may be
generalized to arbitrary spin.
