Letter from estate researcher

Google "Legacy Probate International" and I think you will find your answer.

There are a lot of inheritance scams out there.

This is from an AARP article:
One common version is the bank executor scam, which works something like this: You’ll get a letter or email claiming to be from the executor of the estate of a wealthy person, usually in some foreign country, who recently died and has no known heirs. Somehow, the executor has come up with your name and thinks you might be a distant relative of the deceased. But even if you aren’t, the executor is so eager for a payday that he or she will offer to present you as the next of kin, in exchange for a cut of the estate.
All you’ve got to do is provide the executor some personal data, such as your Social Security number, birth date and bank account number, and send some money to cover fees and taxes. Of course, there isn’t any mystery inheritance out there. If you give the scammer money, you’ll never see it again, and if you hand over sensitive personal data, you may become the victim of identity theft.
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Inheritance scams can be lucrative for criminals. In one recent case prosecuted by the federal government, a ring of Nigerian scammers operating in Madrid and London targeted older Americans over a five-year period, sending them letters that falsely claimed to be from a representative of a Spanish bank. The targets were informed that they were entitled to receive a multimillion-dollar fortune left behind by a distant relative who had died years before — as long as they paid fees for delivery, taxes and payments to keep government officials from asking too many questions. One of the alleged scammers, who was extradited to the U.S. and eventually pleaded guilty, revealed that he had stolen $6 million from 400 victims, according to the Justice Department.
In an older variation of the scheme, a criminal may befriend an older person and pass himself off as an orphan who is in line to inherit a fortune that’s tied up in the probate process. He’ll ask for a loan so he can pay fees and taxes to claim the nonexistent estate, promising to pay back the victim with the money. 

I do kind of feel like some of the verbiage in your letter feels a bit scammy. I think I might consider an attorney to prove it's on up and up.

I have a cousin who died with no heirs. Only his cousins are left, of which I obviously am one. My sister took on the job of being administrator to the estate. We were each contacted by mail by the estate attorney she worked with asking us to sign a paper (and have it notarized) indicating we are ok with her being the administrator. Now my sister has the job of managing any bills and liquidating assets, then dividing the proceeds among any remaining cousins.

How that information fits in with the letter you received I don’t know. Just offering it as possibly helpful.

Unless I've missed it, I can't find any indication of how much their percentage will be.

I wouldn't sign any unsolicited legal document I received in the mail. I'd either do my own research or hire an attorney (selected by me) to investigate.

IF, and that's a big IF, they are not a scam, they will probably want 40% or more of you get as their fee.