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The research enterprise towards achieving high-performance hollow-core photonic crystal fibers has led to impressive advancements in the latest years. Indeed, using this family of fibers becomes nowadays an overarching strategy for building a multitude of optical systems ranging from beam delivery devices to optical sources and sensors. In most applications, an effective single-mode operation is desired and, as such, the fiber microstructure or the light launching setups are typically designed for achieving such a behavior. Alternatively, one can identify the use of large-core multimode hollow-core fibers as a promising avenue for the development of new photonic devices. Thus, in this manuscript, we propose and demonstrate the utilization of a large-core tubular-lattice fiber for accomplishing a speckle-based displacement sensor, which has been built up by inserting and suitably dislocating a single-mode fiber inside the void core of the hollow fiber. The work reported herein encompasses both simulation and experimental studies on the evolution of the multimode intensity distributions within the device as well as the demonstration of a displacement sensor with an estimated resolution of 0.7 {\mu}m. We understand that this investigation identifies a new opportunity for the employment of large-core hollow fibers within the sensing framework hence widening the gamut of applications of this family of fibers.