The sentence seems correct, except that I don't understand what 'intramural' means. To me, 'intramural' means between murals, between walls.
OK, my dictionary explains it: Intramural is within the walls of a building or school, or city. It uses the example of 'intramural football' being played within the school (teams from the same school?).
You could say the same thing with other words, e.g. a student from that same school?