Large earthquakes occurring worldwide have long been recognized to be non Poisson distributed, so involving some large scale correlation mechanism, which could be internal or external to the Earth. We have recently demonstrated this observation can be explained by the correlation of global seismicity with solar activity. We inferred such a clear correlation, highly statistically significant, analyzing the ISI-GEM catalog 1996-2016, as compared to the Solar and Heliospheric Observatory satellite data, reporting proton density and proton velocity in the same period. However, some questions could arise that the internal correlation of global seismicity could be mainly due to local earthquake clustering, which is a well-recognized process depending on physical mechanisms of local stress transfer. We then apply, to the ISI-GEM catalog, a simple and appropriate de-clustering procedure, meant to recognize and eliminate local clustering. As a result, we again obtain a non poissonian, internally correlated catalog, which shows the same, high level correlation with the proton density linked to solar activity. We can hence confirm that global seismicity contains a long-range correlation, not linked to local clustering processes, which is clearly linked to solar activity. Once we explain in some details the proposed mechanism for such correlation, we also give insight on how such mechanism could be used, in a near future, to help in earthquake forecasting.