@Helena ****
I doubt it. I rather believe that school is mistaken. But I can only speak for changing to NON-B for sure. In this case immigration actually suggested I took a CIVID extension, first, so that I would easily have sufficient days on my stamp before changing. They require at least 15 days of permitted stay left to do before doing a visa conversion. You may also encounter two common problems: 1) different offices do things vastly different at times and 2) a culture of where not knowing how can fastly result in saying “cannot” (e.g. with ED visa from schools). Be determined- and it can be done.