A sun-synchronous orbit is a nearly polar orbit around a planet or body, where the satellite passes over the same point on the surface at the same local solar time each orbit. This is achieved by the orbit precessing at the same rate as the planet’s rotation around the sun. Sun-synchronous orbits are commonly used for Earth satellites, especially for imaging and reconnaissance, to maintain consistent lighting conditions.

For a moon to hold a sun-synchronous orbit with respect to its planet, several factors need to be considered:
Existence of a Solar Plane: The moon must have its orbital plane tilted with respect to the ecliptic plane of the planet’s orbit around the sun to maintain a constant local solar time at any given point.
Precession Capability: The orbit must precess to match the rate at which the planet orbits the sun. Such precession can occur due to gravitational interactions, which might be significant if the planet is massive enough (e.g., Jupiter or Saturn), or if there are gravitational perturbations from other moons or celestial objects.
Orbital Period and Plan Configuration: Even with the correct conditions, it can be challenging to maintain this particular orbital resonance due to the distance from the planet and the overall configuration of the moon’s orbit.

In principle, while not impossible, creating and maintaining a sun-synchronous orbit of a moon around its host planet would be highly complex and subject to many gravitational interactions. Such conditions are theoretically conceivable but require very specific configurations and circumstances, potentially involving high levels of perturbation and adjustments. The natural dynamics of celestial bodies make the establishment and stabilization of such orbits quite unlikely without significant gravitational influences or external interventions.