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We synthesize a series of Mn substituted (Li, Fe)OHFeSe superconductor single crystals via a modified ion-exchange method, with the Mn concentration z (the atomic ratio of Mn:Se) ranging from 0 to 0.07. The distribution homogeneity of the Mn element incorporated into the lattice of (Li, Fe)OHFeSe is checked by combined measurements of high-angle-annular-dark-field (HAADF) imaging and electron energy-loss spectroscopy (EELS). Interestingly, we find that the super-conducting transition temperature Tc and unit cell parameter c of the Mn-doped (Li, Fe)OHFeSe samples display similar V-shaped evolutions with the increasing dopant concentration z. We propose that, with increasing doping level, the Mn dopant first occupies the tetrahedral sites in the (Li, Fe)OH layers before starting to substitute the Fe element in the su-perconducting FeSe layers, which accounts for the V-shaped change in cell parameter c. The observed positive correlation between the Tc and lattice parameter c, regardless of the Mn doping level z, indicates that a larger interlayer separation, or a weaker interlayer coupling, is essential for the high-Tc superconductivity in (Li, Fe)OHFeSe. This agrees with our previous observations on powder, single crystal, and film samples of (Li, Fe)OHFeSe superconductors.