I am not sure if spy is correct given the story that is unfolding. Agent provocateur might be more appropriate and likely one who did not know or understand the larger plot....
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Yes, operative(s) given specific assignments on what to instigate/entice/arrange and with whom. All part of a bigger plan in which each mission/assignment is merely a cog.
Spy is a perfectly good term, and I suspect Halper is one of them.