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is every finitely n-presented (S-1)R-module a localization of a finitely n-presented R-module?

Let S be a multiplicative set in a ring R. We can see that every finitely generated (S-1)R-module is a localization of a finitely generated R-module.

Then, more generally, is every finitely n-presented (S-1)R-module a localization of a finitely n-presented R-module ?