  We present a proof that every star-product defined on a Poisson manifold and
written in a given quantum canonical coordinate system is uniquely equivalent
with a Moyal product associated with this coordinate system. The equivalence is
assumed to satisfy some additional conditions which guarantee its uniqueness.
Moreover, the systematic construction of such equivalence is presented and a
formula for this equivalence in a case of a particular class of star-products
is given, to the fourth order in $\hbar$.
