What are my dividend obligations on shares which are pre-borrowed for shorting?

In the case of dividend-paying shares, since shares are only being lent (not sold) by the lender, dividends paid during the borrow belong to the lender who actually owns the shares. The borrower of the shares must pay dividends to the lender in what is called Payment in Lieu of Dividends.

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What are the key dates relating to stock dividends?
What is the Fee Rate?
When are dividends reinvested through the IBKR DRIP program?
Why did I receive a Dividend Gross-Up Payment?