Match Text from one sheet to another and return text

Hello - can someone help me with the attached sample file?

I need to take the name of a school in (sheet 1,column E), search a list of school names on (sheet 2,Column A) to find that name, and return the corresponding cohort name from (sheet 2,column B) to (sheet 1,column F).
I've included 6 examples, but our raw data sheet has 271,509 entries (student info attached to school info).

Thanks!
jb