I'm not sure this is correct or at least a typo ...
On the MO part-year return, you will need to allocate your income to tell MO how much of the income was earned prior to your move. You will claim that income in MS, and you will pay tax on the income in MS.
Don't you mean MO instead of MS in this paragraph? I'm assuming "that income" is referring to MO income earned prior to moving out of state in the last sentence.
Please correct me if I'm wrong.
