It is considered an exceptional case of the Hasemann boundary value problem \[ \Phi^{+}(\alpha(t)) +\frac{\Pi_1(t)}{\Pi_2(t)} G(t)\Phi^{-}(t) + g(t), t\in L, \] with an orientation-preserving shift \(\alpha : L \rightarrow L\) on a Lyapunov closed curve \(L\) on the complex plane. Solvability results are formulated in both homogeneous and inhomogeneous cases. Remark 1. In fact the results are based on the construction which can be used only for analytically continued shift \(\alpha\). Remark 2. The authors have to compare their results with those from the book [\textit{G. S. Litvinchuk}, Solvability theory of boundary value problems and singular integral equations with shifts, Kluwer AP (2000; Zbl 0980.45001)].