When you are on active duty in the military, your home of record is the state where you lived when you joined the military. This doesn't change when you are assigned to serve in another state, unless you ask them to change it.
For instance if he lived with you in Texas when he joined the military, that would be his home of record unless he asks for it to be changed. If you aren't certain, you can check the state listed in box 15 of his military W-2 form. That will show his home of record state.
If you moved in order to accompany him at his new duty station, you also remain a resident of the state you lived in before his service started unless you want to change that. You would pay state taxes as if you lived and worked in that state.
Texas has no state income tax, so it is a good home of record to have.
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