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A geometric construction is provided that associates to a given flat front in$\mathbb{H}^3$ a pair of minimal surfaces in $\mathbb{R}^3$ which are relatedby a Ribaucour transformation. This construction is generalized associating toa given frontal in $\mathbb{H}^3$ , a pair of frontals in $\mathbb{R}^3$ thatare envelopes of a smooth congruence of spheres. The theory of Ribaucourtransformations for minimal surfaces is reformulated in terms of a complexRiccati ordinary differential equation for a holomorphic function. This enablesone to simplify and extend the classical theory, that in principle only worksfor umbilic free and simply connected surfaces, to surfaces with umbilic pointsand non trivial topology. Explicit examples are included.

A connection between flat fronts in hyperbolic space and minimal surfaces in euclidean space