  We give a module-theoretic interpretation of Schiffler's expansion formula
which is defined combinatorially in terms of complete (T,r)-paths in order to
get the expansion of the cluster variables in the cluster algebra of a marked
surface (S,M). Based on the geometric description of the indecomposable objects
of the cluster category of the marked surface (S,M), we show the coincidence of
Schiffler-Thomas' expansion formula and the cluster character defined by Palu.
