  The argument shift method is a well-known method for generating commutative
families of functions in Poisson algebras from central elements and a vector
field, verifying a special condition with respect to the Poisson bracket. In
this notice we give an analogous construction, which gives one a way to create
commutative subalgebras of a deformed algebra from its center (which is as it
is well known describable in the terms of the center of the Poisson algebra)
and an $L_\infty$-differentiation of the algebra of Hochschild cochains,
verifying some additional conditions with respect to the Poisson structure.
