A setup of two bent crystals and a fixed target in the CERN Large Hadron Collider (LHC) could enable the study of the magnetic (MDM) and electric (EDM) dipole moments of short-lived charm baryons with unprecedented accuracy. At the core of the experiment is a bent crystal in which particles of interest, such as the $\Lambda_c^+$ and $\Xi_c^+$ particles, can be confined between the crystalline planes, inducing a deflection that enforces spin precession measurable by detectors. The setup requires a fixed target inside the LHC vacuum to create the charmed baryons. A first crystal serves to split beam halo particles from the circulating beam, allowing the target to be placed at a safe distance. TWOCRYST is a proof-of-principle experiment to be installed in the LHC to demonstrate the feasibility of such an experimental setup. Scheduled for operation in 2025, TWOCRYST aims to deliver crucial data needed to prepare the experiment and gather experience in operating the double-crystal setup. The TWOCRYST test stand features a simplified setup compared to the final experiment but will include all essential components within the LHC beam vacuum: two crystals and one target with the final specifications. Two 2D detectors, one silicon pixel detector and one fiber tracker, installed in movable Roman pots, will allow observation of the crystal channelling and provide important information on the crystal performance at different beam energies up to about 5 TeV. We review the project, all key devices, and the program of machine tests foreseen for TWOCRYST.