If the investor has given you only a promise, then passed away, you have probably had some very bad luck. Check to see whether the investor's heirs might honor his or her wishes. And if that doesn't seem likely, you have to start over.
If the investor has given you written assurances, use these to address those in charge of executing his or her estate. Details of course will depend entirely on what you have as written assurances and in which legal jurisdiction. It is certainly not going to be easy.
I'm sorry to be delivering bad news, but I would guess, without knowing more than what you've included in this email, that the most likely outcome of this is having to start over. Of course if you actually have legal documentation, then your chances might be better.
Tim Berry is the chairman of Eugene, Ore.-Palo Alto Software, which produces business-planning software. He founded Bplans.com and wrote The Plan-As-You-Go Business Plan, published by Entrepreneur Press. Berry is also a co-founder of HavePresence.com, a leader in a local angel-investment group and a judge of international business-plan competitions.