The transfer of information between topological edge states is a robust way of spatially manipulating spatial states in lattice environments. This method is particularly efficient when the edge modes are kept within the topological gap of the lattice during the transfer. In this work, we show experimentally the transfer of photonic modes between topological edge states located at opposite ends of a dimerized one-dimensional photonic lattice. We use a diamond lattice of coupled waveguides and show that the topological transfer is insensitive to the presence of a high density of states in the form of a flat band at an energy close to that of the edge states and prevails in the presence of a hopping impurity. We explore the dynamics in the waveguide lattice using a wavelength-scan method, where different input wavelengths translate into different effective lattice lengths. Our results offer an alternative way to the implementation of efficient transfer protocols based on active driving mechanisms.