We present an extension of our recently presented PreLinK scheme ( J. Chem. Phys. 2013, 138, 134114) for the exact exchange contribution to nuclear forces. The significant contributions to the exchange gradient are determined by preselection based on accurate shell-pair contributions to the SCF exchange energy prior to the calculation. Therefore, our method is highly suitable for massively parallel electronic structure calculations because of an efficient load balancing of the significant contributions only and an unhampered control flow. The efficiency of our method is shown for several illustrative calculations on single GPU servers, as well as for hybrid MPI/CUDA parallel calculations with the largest system comprising 3369 atoms and 26952 basis functions.