A White box penetration test simulates the actions of an attacker who has knowledge of the internal structure and operation of the system or network. This type of test is also known as an
"internal" test.
It is appropriate in this scenario of simulating the malicious actions of a former network administrator, as this person would have knowledge of the internal structure and operation of the network and may have access to privileged information, like credentials, and the knowledge of weak points in the network.
It allows the organization to identify vulnerabilities that an attacker could potentially exploit, and to evaluate the overall security of their network and systems.