Final answer:
The correct process when unauthorized work is added to a project is Perform Integrated Change Control, which handles all change requests and ensures changes are properly approved and documented.
Step-by-step explanation:
The process that most accurately describes the scenario where a team member is performing work that was not originally included in the Work Breakdown Structure (WBS) but was requested by the sponsor is Perform Integrated Change Control. This process involves reviewing all change requests, approving changes, and managing changes to the deliverables, organizational process assets, project documents, and the project management plan. It's a critical part of project management as it ensures that any changes to the project are carefully considered and approved before being implemented, preventing scope creep and ensuring project objectives are met.
The other options mentioned, such as Validate Scope, Control Scope, and Control Quality, do not directly address the specific issue of unauthorized work being added to the project. 'Validate Scope' involves formalizing acceptance of the completed project deliverables, 'Control Scope' refers to the process of monitoring the status of the project and managing changes to the scope baseline, and 'Control Quality' is concerned with ensuring that the project's deliverables meet the quality requirements specified for the project.