Toumei, 45, of California, introduced herself to potential victims as "Lady Catarina Pietra Toumei", according to federal prosecutors.
Their targets appear to have included George Bush
She allegedly offered to broker deals on behalf of the "Guggenheim Bank", which does not exist.
Birnbaum, 67, an Orthodox Jew from Brooklyn, and Zuravel, 45, a Russian native from Queens, are said to have followed up over the phone.
Prosecutors say the pair introduced themselves as "David B Guggenheim" and "Vladimir Z Guggenheim" and offered tantalising investments.
The alleged phoney deals included the sale of $1 billion (£625 million) in diamonds and a stake in a $4 billion (£2.5 billion) Chinese oil deal.
Birnbaum is accused of attempting to broker one deal with the Iraqi Ministry of Oil by representing himself as "chairman of the Guggenheim Bank".
The men's correspondence included documents carrying the Guggenheim logo and email addresses containing the Guggenheim name, prosecutors say.
Ronald Verrochio, the inspector in charge of the New York Office of the United States Postal Inspection Service, called the attempt to swindle investors, "a classic scheme".
It was also short-lived.
Two potential investors contacted Guggenheim Capital, a financial services and investment management holding company linked to Guggenheim heirs, last year with their concerns.
Guggenheim Capital warned the investors that the deal had nothing to do with the Guggenheim family.
It launched a civil suit against Birnbaum, Zuravel and Toumei to stop them using the Guggenheim trademarks.
A judge issued a preliminary injunction and that case is pending.
Meanwhile, the targeted investors co-operated with prosecutors.
This week, Birnbaum and Zuravel were arrested and appeared in a New York court on fraud charges. They face up to 20 years in prison.
Outside court, Zuravel insisted that Birnbaum was a Guggenheim heir. "This is a person who controls a billion, trillion dollars," Zuravel told the New York Post. "He's very rich, trust me."
Toumei turned herself in to a San Diego court on Wednesday.
She told San Diego's 10News that she was anxious to clear her name.
She also faces fraud charges and up to 20 years in prison.
