Most close double helium white dwarfs will merge within a Hubble time due to orbital decay by gravitational wave radiation. However, a significant fraction with low mass ratios will survive for a long time as a consequence of stable mass transfer. Such stable mass transfer between two helium white dwarfs (HeWDs) provides one channel for the production of AM CVn binary stars. In previous calculations of double HeWD progenitors, the accreting HeWD was treated as a point mass. We have computed the evolution of 16 double HeWD models in order to investigate the consequences of treating the evolution of both components in detail. We find that the boundary between binaries having stable and unstable mass transfer is slightly modified by this approach. By comparing with observed periods and mass ratios, we redetermine masses of eight known AM CVn stars by our double HeWDs channel, i.e. HM Cnc, AM CVn, V406 Hya, J0926, J1240, GP Com, Gaia14aae and V396 Hya. We propose that central spikes in the triple-peaked emission spectra of J1240, GP Com and V396 Hya and the surface abundance ratios of N/C/O in GP Com can be explained by the stable double HeWD channel. The mass estimates derived from our calculations are used to discuss the predicted gravitational wave signal in the context of the Laser Interferometer Space Antenna (LISA) project.