You are correct, you can't get any benefits from that second 1095-A, but she can.
If the July through October coverage was only for her in Illinois, she will have to report that on her tax return, and the premium tax credit will be calculated based on her household size and household income, even if you were the one that actually paid for the coverage.
You can work it out with her whether the additional credit on her return is worth more than just a "Thanks Dad!"
