The authors consider a class of Wiener-Hopf operators acting between spaces of Bessel potentials \[ W=r_+A\Bigl| _{H^r_+}:H^r_+ \to H^s_+ (R_+),\quad r,s \in R^n, \] where \(A\) is a translation invariant homomorphism between \(H^r\) and \(H^s\), and \(r_+\) is a restriction operator \(r_+(H^s)\) on \(\overline {R}_+\) and \(H^s (R_+)=\times_{j=1}^n H^{s_j} (R_+), \;s= (s_1,s_2,\dots,s_n)\). Such operators arise with the consideration of some diffraction problems and as rule they are not normal solvable. Passing to lifted Wiener-Hopf operator they obtain the problem with matrix symbol, continuous on the real line and having a jump at infinity. Using the idea of normalization the authors study the possibility for obtaining the explicit formula for solution with help of generalized inverse operators. The main attention is given to the scalar case \((n=1)\) and to the symmetric case \((r=s)\).