  We employ Molecular Dynamics (MD) and Time-Dependent Density Functional
Theory (TDDFT) to explore the fluorescence of Hydrogen-bonded dimer and trimer
structures of Cyclic FF (Phe- Phe) molecules. We show that in some of these
configurations a photon can induce either an \textit{intra}-molecular proton
transfer, or an \textit{inter}-molecular proton transfer that can occur in the
excited S1 and S2 states. This proton transfer, taking place within the
Hydrogen bond, leads to a significant red-shift that can explain the
experimentally observed visible fluorescence in biological and bioinspired
peptide nanostructures with a $\beta$-sheet biomolecular arrangement. Finally,
we also show that such proton transfer is highly sensitive to the geometrical
bonding of the dimers and trimers, and that it occurs only in specific
configurations allowed by the formation of Hydrogen bonds.
