The distribution is reported to the IRS by Fidelity and in theory, they could match it up to your tax returns, or send a letter asking "did someone take the owner's RMD?" but this almost never happens. It's basically on the honor system.
In the future, you and your sister have two requirements: you must each take your own RMDs from your own inherited IRAs each year until the account is closed, and you must spend out the accounts and close them by the end of the 10th year after your father's death.
Someone will need to file your father's final tax return for 2024 (listing income up to, but not after, the date of his death). His income does not include the RMD taken after death, that is the sister's income. The POA dissolves on death, so one of you will have to go to the local probate court and be appointed the administrator or personal representative, to be able to file the final tax return. If he received additional income after his death, that income belongs to his estate, which is a separate legal entity, and there are a couple of ways to handle it, depending on what it is and how much.
