The study of brain functions using fMRI often requires an accurate matching of cortical surface data for comparing brain activation across a population. In this context, several tasks are critical, such as surface in- flation for cortical visualizations and measurements, surface matching and alignment of functional data for group-level analyses. Present methods typically treat each task separately and can be computationally expensive. It takes for example several hours to smooth and match a single pair of cortical surfaces. Furthermore, conventional methods rely on anatomical features to drive the alignment of functional data across individuals, whereas their relation to function can vary across a population. To address these issues, we propose Brain Transfer, a spectral framework that unifies cortical smoothing, point matching with confidence regions, and transfer of functional maps, all within minutes of computation. Spectral methods have the advantage of decomposing shapes into intrinsic geometrical harmonics, but suffer from the inherent instability of these harmonics. This limits their direct comparison in surface matching, and prevents the spectral transfer of functions. Our contributions consist of, first, the optimization of a spectral transformation matrix, which combines both, point correspondence and change of eigenbasis, and second, a localized spectral decomposition of functional data, via focused harmonics. Brain Transfer enables the transfer of surface functions across interchangeable cortical spaces, accounts for localized confidence, and gives a new way to perform statistics on surfaces. We illustrate the benefits of spectral transfers by exploring the shape and functional variability of retinotopy, which remains challenging with conventional methods. We find a higher degree of accuracy in the alignment of retinotopy, exceeding those of conventional methods.