Here is Illinois' rule:
If you were a resident of Illinois during part of the tax year, you are considered a part-year resident and must complete and file Form IL-1040 and Schedule NR if you earned or received income from any source while you were an Illinois resident.
https://www2.illinois.gov/rev/forms/incometax/Documents/currentyear/individual/il-1040-schedule-nr-instr.pdf
Therefore you have to determine the amount of portfolio income you received after becoming an Illinois resident. You became an Illinois resident (and ceased being a CA resident) on the day you began living in your new home in Illinois.