  The entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system
in the presence of intrinsic decoherence is studied. The usefulness of such
system for performance of the quantum teleportation protocol ${\cal T}_0$ and
entanglement teleportation protocol ${\cal T}_1$ is also investigated. The
results depend on the initial conditions and the parameters of the system. For
the product and maximally entangled initial states, increasing the size of
spin-orbit interaction parameter $D$ amplifies the effects of dephasing and
hence decreases the asymptotic entanglement and fidelity of teleportation. We
show that the XY and XYZ Heisenberg systems provide a minimal resource
entanglement, required for realizing efficient teleportation. Also, we find
that for the some special cases there are some maximally entangled states which
are immune to intrinsic decoherence. Therefore, it is possible to perform the
quantum teleportation protocol ${\cal T}_0$ and the entanglement teleportation
${\cal T}_1$ with perfect quality by choosing a proper set of parameters and
employing one of these maximally entangled robust states as initial state of
the resource.
