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State University of New York

Incorrect.

"Companion's" is correct. There's only one companion, so use an aposprophe s. If there were more than one companion, the apostrophe would go at the end of the s (companions'), which is not the case in this sentence.

Mary's suitcases went to Arkansas; her traveling companion's suitcases went to Colorado. Unfortunately, Mary and her companion were going to California.