The complete subject would be "Gale Hawthorne's map".
Explanation:
When looking for complete subject and/or predicate, always try to separate the sentence between noun and verb clauses. Generally the phrase with the verb is the complete predicate, and the phrase with the noun is the complete subject.
So for this sentence, the entire phrase up to the word "borrowed" is the predicate phrase, because the first part of this sentence contains action (verbs).
