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I am very sorry for your loss.
I am not sure who told you that a Power of Attorney survives after death; it does not. Unless the Power of Attorney specifically includes that language that after death, the agent can continue to act in their stead, the power of attorney end when the decedent passes away. Even if such language is included, many third parties will refuse to work with the agent, regardless.
Someone in your situation wants to file for probate. When someone passes away, then their estate has to be distributed. The problem is that without probate - with assets such as titled property or bank accounts (those that do not have a pay on death clause) - this is hard to do. This is because you cannot switch over the assets without an order from the probate court, and simply a Certificate of Death will not do. A Certificate of Death simply states that someone has passed on, but does not give you the right to really do anything in the deceased's name.
So one files probate. Once probate is filed, the Executor of the estate gets something called a Letter of Testament/Administration (hereinafter "Letter"). This Letter will allow the Executor to switch over the assets from the deceased individual to whoever will own the property. It is like a "Power of Attorney," but from the Court. Without that Letter, there is no way to transfer titled property and switch the assets into the hands of the beneficiaries.
If there was a Will, the beneficiaries are decided per the Will. If there was no will, the beneficiaries are decided by default succession law of the state.
If her estate is worth less than about $65,000, then a small estate administration may be filed which is essentially probate via mail - quicker and easier. See HERE.
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