The motivation as to why one would want to give a tidal locked moon a spin is out of the scope of this question. I only want to focus on the feasibility. Suffice to say there could be a few hypothetical reasons such as a night/day cycle for prospective inhabitants.
If there is a moon that is tidally locked, could humans with present or near-future technology create spin on that moon such that the mass of the planet it orbits and the distance the moon is to the planet remain unchanged. That is to say, the only variable we can change is the equipment/technology on the moon to generate spin.
- Present/near future technology (+50 years max)
- Cannot change mass of planet (in the long run)
- Cannot change distance of moon from planet
- Technology includes but is not limited to: propulsion, magnets, megastructure gears, ect
- Unlimited Budget
- 100 year time limit
- near circular orbital eccentricity
- mass of moon is flexible (you can stipulate if your answer works better on small moons or large moons)
- Resulting spin cannot make moon uninhabitable, overly/deadly seismic or otherwise