The active galactic nucleus (AGN) within M87, a giant elliptical galaxy, is responsible for one of the closest kiloparsec-scale relativistic jet to Earth. We unearthed unpublished M87 polarization maps taken with the Faint Object Camera (FOC) aboard the Hubble Space Telescope (HST), obtained between 1995 and 1999. At a rate of one observation per year, we can follow the evolution of the polarized flux knots in the jet. We can thus constrain the time scale of variation of the magnetic field up to a spatial resolution of one tenth of an arcsecond (11.5 pc). After coherently reducing the five observations using the same methodology presented in the first paper of this series, the analysis of polarized maps from POS 1 (base of the jet) and POS 3 (end of the jet) reveals significant temporal and spatial dynamics in the jet's magnetic fields morphology. Despite minimal changes in overall intensity structure, notable fluctuations in polarization degrees and angles are detected across various knots and inter-knot regions. In addition, the emission and polarization characteristics of M87's jet differ significantly between POS1 and POS3. POS1 shows a more collimated jet with strong variability in polarization, while POS3 reveals a thicker structure, a quasi-absence of variability and complex magnetic field interactions. This suggests that the jet may have co-axial structures with distinct kinetic properties. Theoretical models like the jet-in-jet scenario, featuring double helical magnetic flux ropes, help explain these observations, indicating a strong density contrast and higher speeds in the inner jet.