Now that a rocky planet is confirmed to orbit in the habitable zone of our closest stellar neighbor Proxima Centauri, the interest in visiting that system is growing; especially since Breakthrough Starshot proposed a fly-through mission of the Alpha Centauri system by sending a swarm of laser-driven photon sails. While many engineering problems still need to be solved for such a mission to succeed, research has shown that futuristic, theoretical photon-sail configurations can reach the Alpha Centauri system within 75-80 years while also getting captured in a bound orbit about one of the binary stars. This paper investigates trajectories from the binary star system towards planet Proxima b. A mission to Proxima b is scientifically grounded since measurements or pictures could help us better comprehend the evolution of rocky planets and potential life-formation in our Universe. The classical Lagrange points in the binary system (AC-A/AC-B) and the system Proxima Centauri-Proxima b (AC-C/Proxima b) are used to find possible trajectories towards Proxima b. The transfer is divided into a departure phase from AC-A/AC-B and an arrival phase to AC-C/Proxima b. Heteroclinic connections are then exploited using a patched restricted three-body problem method to connect the two phases. A grid search is applied on the optimization parameters to explore the design space, after which a genetic algorithm is applied to further optimize the link, focusing on minimization of the position, velocity, and time error at linkage. Futuristic sail configurations are used, including double-sided reflective sails and lightness numbers up to ß = 1779. The design space exploration shows that a double-sided sail provides little improvement over a one-sided sail, mainly due to the constant sail attitude along the trajectories. Results from the genetic algorithm show that a transfer from the L2-point in the AC-A/AC-B system to the L1-point in the AC-C/Proxima b can be accomplished with a transfer time of 235 years for the one-sided graphene-based sail with a surface of 315x315 m^2 carrying a payload of 10 grams. A transfer from the L2-point in the AC-A/AC-B system to the L3-point in the AC-C/Proxima b, with a smaller one-sided graphene-based sail (75x75 m^2, carrying a payload of 10 grams), results in a transfer time of 1025 years. For both sail configurations, the position error at linkage is kept below 1% of the total travel distance, the velocity error below 1% of the velocity at linkage, and the time error below 1% of the total transfer time.