Even though Friends account (for staff) and Student account are both using the G Suite for Education service, they are on different domains - "@friends.eduhk.hk" (Friends account for staff) and "@s.eduhk.hk" (for student). Staff CANNOT access Google Classroom with their Friends account, as Google Classroom is provided in student domain "@s.eduhk.hk" only.
From Apr 2018, colleagues are provided with two Google accounts to access the G Suite for Education (formerly called Google Apps for Education). The Google account on the student account domain, i.e. firstname.lastname@example.org, has a feature of allowing staff and students to use Google Classroom. The other account on the “friends” domain, i.e. email@example.com, are provided to staff for good so that they could still connected to the University after they leave the University. For details, please visit Google Accounts for Staff.