Low-temperature neutron diffraction and NMR studies of field-induced phases in linarite are presented for magnetic fields $H parallel b$ axis. A two-step spin-flop transition is observed as well as a transition transforming a helical magnetic ground state into an unusual magnetic phase with sine-wave modulated moments $parallel H$. An effective $tilde{J}_1$-$tilde{J}_2$ single-chain model with a magnetization-dependent frustration ratio $alpha_{rm eff} = -tilde{J}_2/tilde{J}_1$ is proposed. The latter is governed by skew interchain couplings and shifted to the vicinity of the ferromagnetic critical point. It explains qualitatively the observation of a rich variety of exotic (for strongly correlated cuprate spin-1/2 Heisenberg systems) longitudinal collinear spin-density wave SDW$_p$ states ($9 geq p geq 2$).
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