(CNN) -

If Cuban intelligence didn't do it, then Sen. Robert Menendez's legal team has a list of other theories about who was behind a prostitution smear that surfaced in 2012 as the powerful senator ran for re-election.

An April letter to the Justice Department lists a litany of possible conspiracies -- in addition to the Cuban spy caper -- behind the mysterious tip that alleged the New Jersey Democrat was a sex tourist who flew to the Dominican Republic to meet underage prostitutes.

The letter from Menendez attorney Stephen Ryan to the Justice Department's public integrity section asks the department to investigate possible "criminal activity intended" to unseat him "and to prevent him from becoming chairman" of the Foreign Relations Committee."

Public integrity prosecutors are leading a corruption probe of whether Menendez violated the law in advocating for campaign donors.

Ryan declined to make his letter public. But CNN reviewed a copy of it and verified its contents with three sources who have seen it.

Cuban intelligence

The letter begins by raising the allegation, sourced to an unnamed "senior government official," that Cuban intelligence agents may have been behind the smear campaign. But Ryan's letter also suggests the possibility of a conspiracy either -- knowingly or unknowingly -- between Cuban intelligence and Republican enemies of the senator.

Among the other theories: That a former U.S. ambassador with a beef against Menendez was the tipster who called himself "Peter Williams" and who shopped the prostitution story to news outlets in Washington, a government watchdog group and to the FBI.

New Jersey politics

Another more complicated theory offered in the letter, citing an unnamed witness: That GOP operative Roger Stone offered the story to the conservative news outlet Newsmax, which refused to publish it.

The same witness allegedly claimed that Stone had a goal in mind -- to ensure Gov. Chris Christie could appoint Menendez's interim successor in the event he had to resign.

"Chris Christie is my ultimate client," the letter says the witness quoted Stone as saying.

Ryan suggests ties to other New Jersey political figures who would want to help sink Menendez's campaign and notes: "Governor Christie's connection to the fraud can be explained from a motive standpoint."

The letter makes no allegation that the governor was part of or even knew of the smear campaign.

Stone denied the allegations in a telephone interview with CNN and called them "patently false."

U.S. officials familiar with the matter told CNN earlier this week that the government was aware of the Cuban espionage allegations and had found no evidence to support it. The Cuban government-run website also dismissed any ties to Cuba.

Corruption probe

The FBI's foray into the prostitution allegations dovetailed with a federal investigation focused on a Menendez donor in Florida, who for years has fought allegations that he overbilled Medicare. Investigators soon began looking into Menendez's relationship with the donor.

Menendez's legal team believes the false prostitution story taints the entire investigation of the senator and wants it looked into further to see where it came from.

"This entire matter began with a campaign of lies to smear Senator Menendez to affect his election and the chairmanship of the Senate Foreign Relations Committee, and those lies included a fraud against the government," Ryan said in a statement.

"The Justice Department has the responsibility to investigate who committed that crime, so when I have received from credible sources information that merited further review, I have sent it to them. We don't know who was responsible for the smear against Senator Menendez, but it is my hope that the Justice Department will demonstrate some urgency in getting to the bottom of it.

"Whoever perpetuated this fraud against the government to smear a United States Senator and potentially influence U.S. policy should be held accountable to the full extent of the law," he added.

Menendez weighs in

Menendez told CNN earlier this week that the Cuban intelligence involvement was plausible.

"Well, let's put it this way, for 22 years, between the House and the Senate, I have had a firm position in opposition to the Cuban regime that violates the human rights - the democracy of the people of Cuba," he said.