Each university and individual course has its own collaboration guidelines. Collaborating with a friend on a part of the assignment could be completely kosher. Not enough information to judge.

From the syllabus and the assignment description: "Students may not work together on graded assignment unless the instructor gives express permission. Collaborating on graded assignments with students from other sections, is a violation of the Stern Honor Code. Similarly, getting help to complete the graded assignments from students that attended the class in the past is also a violation of the Stern Honor Code."

I explicitly prohibited students from working together on individual assignments. There were plenty of group projects for doing so, but for the individual assignments I wanted the students to work alone.

The student clearly violated the Stern Honor Code, and he is openly admitting that.