The West African Monsoon (WAM) system is the main source of rainfall in the agriculturally based region of the Sahel. Understanding transport across the WAM is of crucial importance due to the strong impact of humidity and dust pathways on local cloud formation. However, the description of this transport is challenging due to its 3D complex nature. Lagrangian Coherent Structures (LCS) simplify transport description across the WAM by providing a geometrical partition of the troposphere into domains. Air parcels within each domain have similar dynamical characteristics. LCS make it possible to achieve an integrated vision of transport pathways across this system. Using this approach we unveil new connections in the WAM system. In particular, we identify transport pathways between the Tropical Easterly Jet (TEJ) and the African Easterly Jet (AEJ). Furthermore, the clockwise circulation associated with the divergent upper part of the Sahara heat low is clearly delimitated. Additionally, we show the presence of mixing regions in the AEJ and the lower part of the TEJ that are linked to pathways to sources of dust and humidity.