A quasi-Hopf algebra differs from a Hopf algebra in a weakened version of the coassociativity. (The definition of this ``weak coassociativity'' is motivated by conformal field theory). As well as the ``classical limit'' of a deformation Hopf algebra is a Lie bialgebra, the ``classical limit'' of a quasi-Hopf algebra over \(\mathbb{C}[[h]]\) which is a deformation of a universal enveloping algebra \(U(g)\), is a quasi-Lie bialgebra structure on the Lie algebra \(g\) [see the author, Algebra Anal. 1, No. 6, 114-148 (1989; Zbl 0718.16033)]. However, if the considered quasi-Hopf algebra is quasitriangular, its ``classical limit'' is better described by a symmetric invariant 2-tensor \(t\) on the Lie algebra \(g\). Let \(g\) be a finite dimensional complex Lie algebra and \(t\) a symmetric invariant 2- tensor. Let \(U\) be the \(h\)-adic completion of the enveloping algebra of \(g\otimes \mathbb{C}[[h]]\). In Algebra Anal. 2, No. 4, 149-181 (1990; Zbl 0728.16021), the author proved: {Theorem A:} There exists a quasitriangular quasi-Hopf algebra structure on \(U\), with the usual comultiplication, having \((g, t)\) as its classical limit. The ``weak coassociativity'' is constructed with the help of solutions of the Knizhnik-Zamolodchikov equation. Moreover, {Theorem B:} Up to ``gauge transformations'', any quantization of the pair \((g, t)\) is isomorphic to the one described in Theorem A. The paper under review provides a simpler proof of Theorem B.