After very dense and slow winds erode the outer layer of an asymptotic giant branch (AGB) star down to a thin H-rich layer (≃10−3 M⊙) the star becomes a post-AGB star and evolves at constant luminosity towards hotter temperatures. It may then becomes a planetary nebula nucleus (PNN) at the centre of a planetary nebula (PN). During these phases, the thin H-rich surface layer of the star is eroded by winds. Stardust oxide and silicate grains are recovered from meteorites. The origin of the “Group II grains” that show enrichments in 17O and depletions in 18O is currently explained by invoking the occurrence of some kind of extra-mixing process in AGB stars. We suggest instead that these grains originated from the winds of post-AGB stars and PNN. These winds show the signature of H-burning. We will do this by comparing our predictions from stellar models to the compositions observed in Group II stardust oxide and silicate grains. We find that the composition of the thin H-rich layer lost in the post-AGB and PNN winds is close to that of Group II grains, however the match with the Al ratios needs to be improved. Considering the uncertainities in the 25Mg and 26Al proton capture rates may be helped in this respect.