Deductions & credits

The answer depends on the agreement or understanding between the brother and sister. 

I would consider the transaction to have occurred in 2023 with an IOU as payment. All profit/loss and any gifts would be recognized in 2023.

The loan being paid in 2024 would have no bearing on either tax return, unless there was additional interest paid for 2024. The cash transfer in 2024 is simply paying off a loan made in 2023.

First, let's talk about the inheritance. There usually is no tax on an inheritance, but it usually establishes a "basis". 

The basis is usually the Fair Market Value of the inherited property on the date of death. 

So, lets say the father purchased the house for 150,000 but on the date of death it is worth 230,000. Each half is worth 115,000 so the basis for the brother and the sister is 115,000 each for their respected half. 

Why does this matter? If the property appreciates, lets say to 350,000, each half would be worth 175,000. At this time if the property was sold, the profit would be Capital Gain. In this example, (sold for 350,000) the brother and the sister would each need to claim 60,000 profit. 

Although the property was not "sold" to a third party, the IRS would want the "profit" recognized in 2023 when the brother's half changed hands. 

It gets a bit complicated from here because you don't say if the payment from the sister to the brother for the brother's half was Fair Market Value on the date of the transfer (quit claim deed).

Let's continue with the example above, each half is worth 175,000, but let's say the sister pays 150,000 to the brother. 

The brother has a Capital Gain of 35,000 from this transfer (because his 'basis" was 115,000) and the sister paid 150,000. HOWEVER if it was worth 175,000, the brother has to account for the "missing" 25,000 his sister did not "pay". In this example, the brother would need to claim 25,000 as a gift to the sister. Going forward, the sister would have a "basis" of: 115,000 (when she inherited it) and 175,000 (when she purchased the second half, 150,000 cash and 25,000 gift) so her new basis would be 290,000. If she sold it for more than that, anything over 290,000 would be her Capital Gains (unless there is an exception as her personal residence) 

If the sister paid full value, no gift and no gift tax would need to be addressed, and only the brother would claim the gain on the transfer. 

Could they claim the property and the cash were all gifts? Possibly, but that does not seem to be the intent since it does not "appear" as if the brother simply "gifted" half the house to the sister. If the IRS asked, it would be difficult to prove that the brother was in a better financial position than his sister in 2023, so he gifted the property, while one year later the sister was in a better financial position than the brother and gifted him cash. 

IRS link on Inherited Property