Should be thrown out of court
This case should fail on standing. As I understand it, the animal was wild and therefore not owned. Under US law, only something recognized as a 'person' (human or corporation, basically) can own a copyright, therefore only a 'person' can be damaged by violation of said copyright, therefore only a 'person' can sue over it. Since no 'person' owns the monkey, no 'person' can be given standing to make cause for the monkey and PETA is actually representing a client relationship that is not present and would not be legal even if it were.
I sincerely hope the judge dismisses the case with prejudice and someone sues PETA for wasting everyone's time and causing material damage to a person's career. *THAT* is a lawsuit for which there is standing, material damage, and a clear train of evidence.