<p>We theoretically investigate the squeezing and entanglement properties of two spatially separated magnon modes in a dual-cavity system. Each cavity contains a microwave (MW) field mode coupled to the magnon mode of a yttrium iron garnet (YIG) sphere. The cavities are coupled to each other and driven by a two-mode squeezed vacuum MW field, which facilitates the transfer of quantum correlations to the magnon modes. Our results show that the magnon modes exhibit squeezing, with the degree of squeezing depending on the intensity of the injected squeezed field. Using the Hillery-Zubairy criterion, we quantify the entanglement between magnons, revealing that stronger cavity-magnon coupling enhances their entanglement. Notably, the squeezed field significantly enhances magnon-magnon entanglement, highlighting its crucial role in mediating and controlling non-classical correlations in the hybrid system.</p>