Accurate simulations of vibrational molecular spectra require precise molecular force fields, at least with cubic and quartic anharmonic corrections beyond the harmonic limits. Generation of such force field terms becomes computationally prohibitive for larger molecules. In this work, an alternate possibility is explored, where approximate anharmonic force field components are obtained from molecular fragments. Transferability properties of the cubic and incomplete quartic fields are discussed and tested on model oligoproline molecules. Automatic transfer schemes including cubic, two and three atomic quartic force constants are developed and implemented. The results indicate that the main vibrational interactions in molecules are local and the anharmonic constants are mostly well amendable to the transfer. Exact anharmonic normal mode force fields of larger molecules compared very well to those obtained from smaller molecular parts. The most important changes in vibrational spectra caused by the anharmonic interactions could be reproduced with two and three atomic force field terms. The transfer scheme thus provides molecular anharmonic force fields without a significant loss of accuracy and brings significant savings of computer time and memory needed to generate molecular vibrational energies and spectra.