It is proved that the global (\(\forall\, x\in\mathbb{R})\) inverse Miura transformation is possible, more precisely, it is proved that the Riccati equation \(v(x,t)=u_x(x,t)+u^2(x,t)\) is solvable for all \(x\in\mathbb{R}\), under the boundary conditions \(u(x,t)\sim C_1\) (resp. \(C_2)\) for \(x\to -\infty\) (resp. \(x\to \infty)\), \(v(x,t)\sim a^2\) (resp. \(b^2)\) for \(x\to -\infty\) (resp. \(x\to \infty)\) (where \(c_1=\pm a\), \(c_ 2\pm b\), \(a>0\), \(b>0)\) and the summability conditions \[ \int^{0}_{- \infty}(1+| x|)| v(x)-a^2| \,dx+\int^{\infty}_{0}(1+x)| v(x)-b^2| \,dx0,\quad \forall \phi (x)\in C_0^{\infty}(\mathbb{R}). \]