Please accept my condolences on the demise of your husband.
You should contact an attorney.
In some cases, partnership agreements trump rights of succession upon death, insofar as the partnership is concerned.
But, you should be entitled to monetary compensation.
If his partner won't voluntarily recognize your claim, it'll take a court action and a judge's order to accomplish it.
In some cases, businesses get dissolved upon the death of one or more owners/partners.
Sorry, discuss this with an attorney and be sure to take all the documents you possess about the business, especially the articles of partnership.
This site explains intestate succession in HI.
The important thing to note, your state requires a probate case to be opened.
Again, another reason to retain an attorney.
http://www.sklslaw.com/blog/intestate-succession-in-hawaii
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http://www.meyersonlawfirmblog.com/2013/09/19/hawaii-wrongful-death-laws/
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