A new chrome book is connected in a school's network.

For managing the FortiClient web filter extension installed on the Google Chromebook endpoint, the EMS administrator can use the following component:

FortiClient EMS (Enterprise Management Server)is designed to manage and control multiple FortiClient installations across various endpoints.

EMS provides centralized management for endpoint policies, including web filtering configurations.

The EMS administrator can configure and enforce web filter policies on Chromebooks through the EMS console.

Therefore, FortiClient EMS is the correct component for managing the web filter extension on Google Chromebook endpoints.

References

FortiClient EMS 7.2 Study Guide, Chromebook Management Section

Fortinet Documentation on FortiClient EMS and Web Filtering for Chromebooks