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Perovskite films have rapidly emerged as leading active materials in optoelectronic devices due to their strong optical absorption, high carrier mobility and ease of fabrication. Whilst proving to be promising materials for solar cells and light-emitting diodes, another application of perovskites which makes effective use of their unique properties is sensitisation for photon upconversion. Consisting of a bulk perovskite sensitiser alongside an adjacent organic semiconductor film, the upconverting system can absorb multiple low-energy photons to emit high-energy photons. In this work, density functional theory, in conjunction with GW theory, is utilised to investigate the electronic structure at the MAPbI$_3$/rubrene interface for different surface terminations of MAPbI$_3$. From this investigation, we reveal that the surface termination of the perovskite layer greatly affects the charge density at the interface and within the rubrene layer driven by the formation of interfacial dipole layers. The formation of a strong interfacial dipole for the lead-iodide terminated perovskite alters the band alignment of the heterojunction and is expected to facilitate more efficient hole transfer. For the perovskite surface terminated with the methylammonium iodide layer, the highest occupied molecular orbital of the adjacent rubrene layer lies deep within the perovskite band gap. This termination type is further characterized by a lower density of states near the band edges thereby acting as a spacer which is anticipated to decrease the probability of charge transfer across the interface. Thus based on our results, PbI$_2$-terminated perovskite surfaces are predicted to be favourable for applications where hole transfer to a rubrene layer is ideal, highlighting the significance of surface termination for all systems where the electronic environment at the interface is crucial to performance.