Relative regular Riemann-Hilbert correspondence

In previous works by the last named authors, the notion of regularity for a relative holonomic D-module has been introduced, as well as that of relative constructible complex, and it has been proved that, if the parameter space has dimension one, the solution functor from the bounded derived category of relative modules with regular holonomic cohomology to that of relative constructible complexes is essentially surjective, by constructing a right quasi-inverse functor. In the present article, we prove that this functor satisfies the left quasi-inverse property.