Hello -

My fiance' recently moved to Texas from Louisiana. She worked in both states. She also received unemployment in Louisiana as for time she wasn't working while residing there. How does she file as Louisiana has state taxes, and Texas does not.

When did you move from Louisiana? If you were in the state for more than 183 days, you may be resident of the state. Check the requirements at state website.
If you are resident, you must report worldwide income for the year.
If you are part year resident, then report income that you earned while in the state.
Read Your U.S. Tax Return: Working or Living in Two or More states