Your gut is correct. They want to get into your financial account or even to get them to send you money. These type scams have been going on for a long time.
This answer is not intended to provide you with specific legal advice regarding your situation, or to create any attorney-client relationship.
You are right to be suspicious. If you are asked for any kind of personal information, do not provide it. And if you are asked to pay anything to anyone, don't do it. If by some chance it is a real bequest, that will eventually become clear. However, most likely this is a scam, as you suspect.
Your gut is correct. That's an obvious scam.
Read about it at http://www.scamdex.com/ScamTipReport.php?num=2097 and
also here on AVVO at http://www.avvo.com/legal-answers/i-received-an-email-stating-i-have-been-named-bene-692405.html
They want to loot your bank account. Don't talk to them.