Ingrid, from Germany, worked part of the year at the local university in California. She gave the university Form 8233 and they properly applied her treaty benefit. In August, Ingrid moved to Illinois and began the fall semester at the local university. She gave Form 8233 to the university in Illinois. However, the Illinois university was not aware that Ingrid had already exempted part of her income in California. At the end of the year, Ingrid's taxable wages were calculated as follows:

Income and Federal Taxes Withheld	Amount
W-2 California university wages, taxes withheld	$380
1042-S Code 20 California university	$9,000
W-2 Illinois university wages, taxes withheld	$1,685
1042-S Code 20 Illinois university	$9,000
Total wages	$20,065
Allowable treaty benefit	$9,000
Taxable wages	$11,065

Would Ingrid receive a refund of federal income taxes withheld if her treaty benefit was applied correctly at both colleges?