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NMR line shape and its Fourier transform, free induction decay (FID) are essential sources of structural and dynamic information in diverse materials [1]. Multiple quantum NMR spectroscopy [2] created new possibilities for the problem under consideration, both experimental and theoretical [3]. Recently we have shown [4] that proton zigzag chains in single crystals of hambergite can be considered as isolated one-dimensional systems. The dipole-dipole interaction (DDI) coupling constants of the nearest neighbors in hambergite can be equal or alternate, taking two different values, depending on the orientation of the crystal. Investigation of the one-dimensional spin systems is beneficial since there exist exactly solvable theoretical models, in particular [3]. Earlier we have investigated the MQ dynamics in homogeneous quasi-one-dimensional spin chains in fluorapatite (FAp) [5]. The regularity of the FAp crystal lattice creates identical dipolar couplings among the nearest spins in the chain while the interactions with other spins are significantly smaller and can be ignored, at least in the first approximation. In the present study we investigate the MQ dynamics in the inhomogeneous quasi-one-dimensional spin chains of protons in hambergite. The zig-zag arrangement of the spins in the chains causes the dipolar coupling constants to alternate between two values when passing along the chain.