An undeniable signature scheme is a form of digital signature in which the signer maintains control over the verifiability of signatures. In particular, verification can only be performed by an authenticated verifier with the explicit cooperation of the signer. In this work, we present a post-quantum undeniable signature scheme constructed over module lattices. Our construction builds upon the GPV framework and derives its security from the hardness of the SIS and LWE problems. We formally establish that the proposed scheme satisfies all the required security properties. Moreover, this work provides a concrete implementation of a lattice-based undeniable signature scheme, evaluated across different parameter sets. The choice of the module-lattice setting over the ring-lattice variant is motivated by the additional flexibility it offers in parameter selection.