T-cells massively restructure their internal architecture upon reaching an antigen-presenting cell (APC) to form the immunological synapse (IS), a cell-cell interface necessary for efficient elimination of the APC. This reorganization occurs through tight coordination of cytoskeletal processes: actin forms a peripheral ring, and dynein motors translocate the centrosome toward the IS. A recent study proposed that centrosome translocation involves a microtubule (MT) bundle that connects the centrosome perpendicularly to dynein at the synapse center: the "stalk." The synapse center, however, is actin-depleted, while actin was assumed to anchor dynein. We propose that dynein is attached to mobile membrane anchors, and investigate this model with computer simulations. We find that dynein organizes into a cluster in the synapse when translocating the centrosome, aligning MTs into a stalk. By implementing both a MT-capture-shrinkage and a MT-sliding mechanism, we explicitly demonstrate that this organization occurs in both systems. However, results obtained with MT-sliding dynein are more robust and display a stalk morphology consistent with our experimental data obtained with expansion microscopy. Thus, our simulations suggest that actin organization in T-cells during activation defines a specific geometry in which MT-sliding dynein can self-organize into a cluster and cause stalk formation.