Nonlocal coupling, as an important connection topology among nonlinear oscillators, has attracted increasing attention recently with the research boom of chimera states. So far, most previous investigations have focused on nonlocally coupled systems interacted via similar variables. In this work, we report the evolutions of dynamical behaviors in the nonlocally coupled Stuart-Landau oscillators by applying conjugate variables feedback. Through rigorous analysis, we find that the oscillation death (OD) can convert into the amplitude death (AD) via the cluster state with the increasing of coupling range, making the AD regions to be expanded infinitely along two directions of both the natural frequency and the coupling strength. Moreover, the limit cycle oscillation (OS) region and the mixed region of OD and OS will turn to anti-synchronization state through amplitude-mediated chimera. Therefore, the procedure from local coupling to nonlocal one implies indeed the continuous enhancement of coherence among neighboring oscillators in coupled systems.