The most general expression of the axis-translation theorem (parallel-axis theorem)for the 2-order scalar charge moment of a charge system around any two parallel axes is deduced. The generalized axis-translation theorem of the magnetic moment of a rotational charged body around any two parallel axes is derived through the simple proportionate relation between the fixed-axis magnetic moment and the 2-order scalar charge moment for the same charge system. The specific conclusions of axis translation theorem are demonstrated and discussed under three cases：1)the total charge (0-order charge moment)is zero;2)the electric dipole moment (1-order charge moment)is zero;3)both the total charge and electric dipole moment are zero. The ambiguities are clarified and the mistakes in some references are corrected.