The crystallinity of graphene flakes and their orientation with respect to the Cu(111) substrate are investigated by means of low‐energy electron microscopy (LEEM). The interplay between graphene and the metal substrate during chemical vapor deposition (CVD) introduces a restructuring of the metal surface into surface facets, which undergo a step bunching process during the growth of additional layers. Moreover, the surface facets introduce strain between the successively nucleated layers that follow the topography in a carpet‐like fashion. The strain leads to dislocations in between domains of relaxed Bernal stacking. After the transfer onto an epitaxial buffer layer, the imprinted rippled structure of even monolayer graphene as well as the stacking dislocations are preserved. A similar behavior might also be expected for other CVD grown 2D materials such as hexagonal boron nitride or transition metal dichalcogenides, where stacking relations after transfer on a target substrate or heterostructure could become important in future experiments.