  Let $M$ be an $n$-dimensional Frobenius manifold. Fix
$\kappa\in\{1,\dots,n\}$. Assuming certain invertibility, Dubrovin introduced
the Legendre-type transformation $S_\kappa$, which transforms $M$ to an
$n$-dimensional Frobenius manifold $S_\kappa(M)$. In this paper, we show that
these $S_\kappa(M)$ share the same monodromy data at the Fuchsian singular
point of the Dubrovin connection, and that for the case when $M$ is semisimple
they also share the same Stokes matrix and the same central connection matrix.
A straightforward application of the monodromy identification is the following:
if we know the monodromy data of some semisimple Frobenius manifold $M$, we
immediately obtain those of its Legendre-type transformations. Another
application gives the identification between the $\kappa$th partition function
of a semisimple Frobenius manifold $M$ and the topological partition function
of $S_{\kappa}(M)$.
