  We consider deformations of a differential system with Poincare' rank 1 at
infinity and Fuchsian singularity at zero along a stratum of a coalescence
locus. We give necessary and sufficient conditions for the deformation to be
strongly isomonodromic, both as an explicit Pfaffian system (integrable
deformation) and as a non linear system of PDEs on the residue matrix A at the
Fuchsian singularity. This construction is complementary to that of [13]. For
the specific system here considered, the results generalize those of [26], by
giving up the generic conditions, and those of [3], by giving up the Lidskii
generic assumption. The importance of the case here considered originates form
its applications in the study of strata of Dubrovin-Frobenius manifolds and
F-manifolds.
