I don't understand why you would be prohibited unless there was something that defamed someone living (libel).
This sounds more like a family issue than a law issue. Your best bet is probably to talk it over with your sisters. If needed, you could all agree to a community mediation to try to help you.
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This is more of an intellectual property and probate issue than a family law issue. I've redirected your post to the IP forum. Good luck.
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This issue involves copyright law and wills/probate. Copyright subsists in original works of authorship fixed in a tangible medium of expression. Copyright rights attach as soon as the original work of authorship is fixed in a tangible medium of expression. In other words, as soon as your mother wrote the letters, she owned the copyright rights in and to those letters.
Copyright gives exclusive rights to the copyright owner. These exclusive rights are: reproduction, adaptation, distribution, performance, and display (and there are also exclusive rights associated with sound recordings). Copyright rights can be bequeathed.
It appears that you have possession of the letters. But possession of the letters does not equal ownership of the copyrights in those letters.
The copyright may or may not have expired. That is a whole other matter that needs to be addressed.
As you can see, there are many, many issues involved (I have not even mentioned many of them). So you really need to speak with an experienced copyright attorney who can learn all of the specific facts of your situation and can give you tailored advice on whether or how you could move forward with your project.
In the end, the answer to your question of "Can I" publish your deceased mother's letters may be a mixture of law and family relations. Contact an experienced copyright law.
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