  It is known that any Poisson manifold can be embedded into a bigger space
which admites a description in terms of the canonical Poisson structure, i.e.,
Darboux coordinates. Such a procedure is known as a symplectic realization and
has a number of important applications like quantization of the original
Poisson manifold. In the present paper we extend the above idea to the case of
quasi-Poisson structures which should not necessarily satisfy the Jacobi
identity. For any given quasi-Poisson structure $\Theta$ we provide a recursive
procedure of the construction of a symplectic manifold, as well as the
corresponding expression in the Darboux coordinates, which we look in form of
the generalized Bopp shift. Our construction is illustrated on the exemples of
the constant $R$-flux algebra, quasi-Poisson structure isomorphic to the
commutator algebra of imaginary octonions and the non-geometric M-theory
$R$-flux backgrounds. In all cases we derive explicit formulae for the
symplectic realization and the generalized Bopp shift. We also discuss possible
applications of the obtained mathematical structures.
