Static binary lifting is essential in binary rewriting frameworks. Existing tools overlook the impact of External Function Completion (EXFC) in static binary lifting. EXFC recovers the declarations of External Functions (EXFs, functions defined in standard shared libraries) using only the function symbols available. Incorrect EXFC can misinterpret the source binary, or cause memory overflows in static binary translation, which eventually results in program crashes. Notably, existing tools struggle to recover the declarations of mangled EXFs originating from binaries compiled from C++. Moreover, they require time-consuming manual processing to support new libraries.This paper presents EFACT, an External Function Auto-Completion Tool for static binary lifting. Our EXF recovery algorithm better recovers the declarations of mangled EXFs, particularly addressing the template specialization mechanism in C++. EFACT is designed as a lightweight plugin to strengthen other static binary rewriting frameworks in EXFC. Our evaluation shows that EFACT outperforms RetDec and McSema in mangled EXF recovery by 96.4% and 97.3% on SPECrate 2017.Furthermore, we delve deeper into static binary translation and address several cross-ISA EXFC problems. When integrated with McSema, EFACT correctly translates 36.7% more benchmarks from x86-64 to x86-64 and 93.6% more from x86-64 to AArch64 than McSema alone on EEMBC.