  In the first part of this paper, we give a new analytical proof of a theorem
of C. Sabbah on integrable deformations of meromorphic connections on $\mathbb
P^1$ with coalescing irregular singularities of Poincar\'e rank 1, and
generalizing a previous result of B. Malgrange. In the second part of this
paper, as an application, we prove that any semisimple formal Frobenius
manifold (over $\mathbb C$), with unit and Euler field, is the completion of an
analytic pointed germ of a Dubrovin-Frobenius manifold. In other words, any
formal power series, which provides a quasi-homogenous solution of WDVV
equations and defines a semisimple Frobenius algebra at the origin, is actually
convergent under no further tameness assumptions.
