OK - that's what I understand as well. So at this point, the S Corp makes the election and pays the PTE tax. Then the shareholder includes that tax credit on his 2021 Form IL-1040. No tax benefit for the S Corp (and ultimately the shareholder on his personal tax return) until 2022 because the payments are being made in Jan/Feb 2022.

Then the S Corp will need to make estimated tax payments in 2022 based on the expected 2022 PTE tax. 

So, would the S Corp be able to claim a deduction on the 2022 partnership for both the PTE tax that is due now (for the 2021 tax year) as well as for the estimated tax payments being made for the PTE tax that is associated with the 2022 tax year? That is, basically deducting two years worth of PTE taxes in 2022. Does that sound correct?