Finding the right synonym for "exact counterpart" depends on the context and purpose of use. Some of the synonyms that could be used in place of the phrase "exact counterpart" include "mirror image," "perfect replica," "twin," "clone," "carbon copy," or "double." However, each of these synonyms has subtle differences in their connotations of meaning, which can shift the nuance. For instance, "mirror image" suggests a close resemblance or reflection of the original, while "clone" implies a perfect genetic copy of the original. Ultimately, selecting the most accurate synonym for "exact counterpart" requires understanding the context and precise meaning of the text or context in which they are used.