Solventless synthesis and processing of Metal Organic Frameworks (MOFs) is critical to implement these materials in applied technologies. Vapour phase synthesis of MOF thin films is particularly suitable for such applications, but challenging compared to the conventional solution based methods. It is therefore compelling to advance and widen the vapour phase synthesis of MOF thin films. Crystalline copper terephthalate MOF thin films are grown in the vapour phase by means of atomic and molecular layer deposition (ALD/MLD) on different kinds of substrates. Expanding from the pioneering work, the formation of the 3D phase is clearly evidenced for the first time and the adaptability of the process to several kinds of substrates is revealed. A directional film growth is observed at the early stage of the ALD/MLD process leading to oriented MOF crystallites on a surface, when isotropical growth proceeds with the increasing number of ALD/MLD cycles. Notably, this study primarily demonstrates a heteroepitaxial growth achievable in the vapour phase by using DMOF-1 single crystals as the starting surface with a lattice matching topology. Such an approach offers an appealing pathway to develop MOF on MOF superlattice materials in the vapour phase.