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Thank you for your question.
First, yes, your mother should write a will. It makes things much easier when a person does.
That said, if a person dies without a will, that person's property passes to their heirs via the intestate rules. Your mother owns a property interest in a partnership. You will be entitled to that interest or the liquidated value of that interest, depending upon how the partnership agreement is worded. Generally, the partner's interest does not pass to another person, but instead, the partnership pays the next of kin the value of that partnership interest.
I hope this helps.
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