Magma transport through the Earth's crust occurs dominantly via sheet intrusions, such as dykes and cone-sheets, and is fundamental to crustal evolution, volcanic eruptions and geochemical element cycling. However, reliable methods to reconstruct flow direction in solidified sheet intrusions have proved elusive. Anisotropy of magnetic susceptibility (AMS) in magmatic sheets is often interpreted as primary magma flow, but magnetic fabrics can be modified by post-emplacement processes, making interpretation of AMS data ambiguous. Here we present AMS data from cone-sheets in the Alnö carbonatite complex, central Sweden. We discuss six scenarios of syn- and post-emplacement processes that can modify AMS fabrics and offer a conceptual framework for systematic interpretation of magma movements in sheet intrusions. The AMS fabrics in the Alnö cone-sheets are dominantly oblate with magnetic foliations parallel to sheet orientations. These fabrics may result from primary lateral flow or from sheet closure at the terminal stage of magma transport. As the cone-sheets are discontinuous along their strike direction, sheet closure is the most probable process to explain the observed AMS fabrics. We argue that these fabrics may be common to cone-sheets and an integrated geology, petrology and AMS approach can be used to distinguish them from primary flow fabrics.