If my daughter lived in NJ for two months of 2023 and then moved to PA but only had income for the last five months of 2023 working in NJ. What taxes must she file?

New Jersey and Pennsylvania have a reciprocal agreement, that means the Taxpayer pays tax to the state in which they live.

If your daughter was living in PA when she earned her income, your daughter files a Part-Year resident PA return (if that's where she lived when she earned the income working in New Jersey)  and pays only PA tax on the income she earned working in NJ. If no NJ tax was withheld, she needn't file a NJ return. (unless there are other factors, like rental income)

If she lived in NJ when she earned some income, she would file part-year resident for New Jersey and allocate only what she earned while a resident. 

If she lived in PA while working in NJ, and NJ tax was withheld, she'll need to file a Part-Year NJ return, allocate zero income to NJ and get the state tax withheld refunded.