An experimental laboratory set of samples of composite heterogeneous anion-exchange membranes was obtained by us for the development of our original method of polycondensation filling. Anion-exchange membranes were prepared on plasma-treated and non-plasma-treated polyester fiber fabrics. The fabric was treated with low-temperature argon plasma at a power of 400 W for 10 min at a pressure of 5 × 10−5 mbar. On the surface and bulk of the polyester fiber, a polyfunctional anionite of mixed basicity was synthesized and formed. The anion-exchange membrane contained secondary and tertiary amino groups and quaternary ammonium groups, which were obtained from polyethylene polyamines and epichlorohydrins. At the stage of the chemical synthesis of the anion matrix, oxidized nanoparticles (~1.5 wt.%) of silicon, nickel, and iron were added to the monomerization composition. The use of ion-plasma processing of fibers in combination with the introduction of oxidized nanoparticles at the synthesis stage makes it possible to influence the speed and depth of the synthesis and curing processes; this changes the formation of the surface morphology and the internal structure of the ion-exchange polymer matrix, as well as the hydrophobic/hydrophilic balance and—as a result—the different operational characteristics of anion-exchange membranes.