We investigate the magnetic characteristics of a persistent coronal hole (CH) extracted from EUV imagery using Heliospheric and Magnetic Imager filtergrams over the period 2012 Febmary-October. The magnetic field, its distribution, and the magnetic fine structure in the form of flux tubes (FTs) are analyzed in different evolutionary states of the CH. We find a strong linear correlation between the magnetic properties (e.g., signed/unsigned magnetic field strength) and the area of the CH. As such, the evolutionary pattern in the magnetic field clearly follows a three-phase evolution (growing, maximum, and decaying) as found from EUV data (Part I). This evolutionary process is most likely driven by strong FTs with a mean magnetic field strength exceeding 50 G. During the maximum phase they entail up to 72% of the total signed magnetic flux of the CH, but only cover up to 3.9% of the total CH area, whereas during the growing and decaying phases, strong FTs entail 54%-60% of the signed magnetic flux and cover around 1%-2% of the CH's total area. We conclude that small-scale structures of strong unipolar magnetic field are the fundamental building blocks of a CH and govern its evolution.