The Atlantic Meridional Overturning Circulation (AMOC) plays a crucial role in the global climate system. Various studies report both ongoing and projected reductions in AMOC strength, with important implications for climate and society. While Stratospheric Aerosol Injection (SAI) has been proposed to mitigate some impacts of a warming climate, model simulations disagree whether it could also be successful in ameliorating the projected AMOC decline. Using SAI sensitivity simulations with the Community Earth System Model, we demonstrate that whether SAI could restore AMOC depends on the details of SAI realization, particularly its latitude(s). Specifically, Northern-hemispheric SAI initially impacts upper-ocean densities in the North Atlantic through changes in surface heat flux and temperature, ultimately preventing AMOC decline. On the other hand, Southern-hemispheric SAI does not substantially impact AMOC strength even though global mean cooling is achieved. We show that different processes play different roles in determining the AMOC response between the initial (~10-15 years) and longer timescales, with the former dominated by the direct SAI effect and the latter influenced by feedbacks from AMOC adjustments. These processes may also offset each other, leading to a relatively stable evolution of AMOC under each SAI realization and a small, yet substantially different, subset of potential AMOC responses. Overall, our results demonstrate the potential for SAI to help avoid climatic tipping points, but also highlight the need to understand the dependence of the outcomes on the specific SAI realization as well as for a better process-based understanding of the many factors influencing such outcomes.