Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic reasoning. HEX-programs extend ASP with external atoms for access to arbitrary external sources, which can also introduce constants that do not appear in the program (value invention). In order to determine the relevant constants during (pre-)grounding, external atoms must in general be evaluated under up to exponentially many possible inputs. While program splitting techniques allow for eliminating exhaustive pre-grounding, they prohibit effective conflict-driven solving. Thus, current techniques suffer either a grounding or a solving bottleneck. In this work we introduce a new technique for conflict-driven learning over multiple program components. To this end, we identify reasons for inconsistency of program components wrt. input from predecessor components and propagate them back. Experiments show a significant, potentially exponential speedup.