Fidelity Investments should be able to split up your mother's investments in accordance with your mother's wishes. Then both you and your sister will have your own Fidelity Investment account to report your own income earned on the investments. It is possible that the investments will generate taxable income and taxes will be due next year.
In most cases, proceeds paid out from a life insurance policy is not taxable income. See this TurboTax Help.
Contact legal counsel to assist you and your sister with administering your mother's will and dealing with all of these issues and other issues that may arise.
My sympathy to your for your loss.
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