Answer:
"The author"
Step-by-step explanation:
According to Thesaurus.com, "An appositive is a noun or noun phrase that clarifies, identifies, describes, or otherwise renames another noun or noun phrase." An example of an appositive could be "My friend" in the sentence My friend Rachel loves to draw.
Based on this information, "The author" is the appositive phrase in the given sentences. Hopefully that's helpful. :)