An algebraic version of the Poincare construction

The Poincare construction in CR geometry allows to estimate the dimension of the stabilizer of the Lie algebra of infinitesimal holomorphic automorphisms of a germ of an arbitrary CR manifold by the dimension of the stabilizer of the corresponding algebra of the model surface of the germ. We give a negative answer to the following natural question. Does there exist an algebraical version of the Poincare construction, i.e., is it true that the stabilizer of the automorphisms algebra of a germ of the CR manifold can be embedded into the stabilizer of the algebra of its model surface as a Lie subalgebra? We also give a negative answer to the corresponding question for the whole automorphisms algebra.