John Eastman, the conservative lawyer whose plan to block congressional certification of the 2020 election spectacularly failed on Jan. 6, 2021, emailed two weeks later arguing that pro-Trump forces should sue to continue looking for the alleged voter fraud admitted they hadn’t found it.

On Jan. 20, 2021, hours after President Biden’s inauguration, Mr. Eastman emailed Rudolph W. Giuliani, personal attorney for former President Donald J. Trump, and suggested that they review the result of the Georgia runoff for two Senate seats won on Jan. 5 by Democrats.

“Many of us have now staked our reputation on allegations of voter fraud and this would be one way to gather evidence,” Mr Eastman wrote in the previously unreleased email, which was also shared with others, including a top campaign adviser Trump . “If we get evidence of fraud on January 5, it will likely prove fraud on November 3, corroborating President Trump’s claims and serving as a strong bulwark against the Senate impeachment process.”

The email, which was reviewed by The New York Times and authenticated by people who worked on the Trump campaign at the time, is the latest evidence that even some of Mr. Trump’s most ardent supporters knew their unfounded Allegations of a widespread vote had failed to prove fraud – but wanted to continue their efforts to delegitimize the result even after Mr Biden took office.

Mr Eastman’s message also underscored that he didn’t take on the job of keeping Mr Trump in office out of conviction: he asked Mr Giuliani for help collecting a $270,000 bill he owed the Trump Campaign had been sent the previous day for his legal advice.

The charges included $10,000 a day for eight workdays in January 2021, including the two days leading up to Jan. 6 when Mr. Eastman and Mr. Trump at meetings in the Oval Office unsuccessfully tried to pressure Vice President Mike Pence to go along with it the plan to block congressional certification of the January 6 Electoral College results. (Mr. Eastman appears never to have been paid.)

An attorney for Mr. Eastman did not respond to a request for comment.

The disclosure of the email comes as the Justice Department ramps up its criminal investigation into efforts to overturn the 2020 election. Patrick F. Philbin, who was Assistant White House Counsel under Mr. Trump, has received a grand jury subpoena in the case, a person familiar with the situation said.

Mr. Philbin is the youngest senior former White House official known to appear before the grand jury. Others include his former boss Pat A. Cipollone, who as White House Counsel, along with other White House Counsel, argued against some of the more extreme moves proposed by Mr. Trump and his advisers as they tried to stay in power .

Previous subpoenas to a number of people had sought information about outside attorneys, including Mr. Eastman and Mr. Giuliani, who were advising Mr. Trump and furthering his efforts to reverse the findings.

In June, federal agents armed with a search warrant seized Mr Eastman’s phone and stopped him as he was leaving a New Mexico restaurant.

Key revelations from the January 6 hearings

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impeach Trump. The House of Representatives committee investigating the Jan. 6 attack presents a comprehensive account of President Donald J. Trump’s efforts to overthrow the 2020 election. Here are the main themes that have emerged from eight public hearings so far:

Testifying before the House committee investigating the Jan. 6 attack on the Capitol, another White House attorney, Eric Herschmann, said that on Jan. 7, 2021, Mr. Eastman brought with him the idea of ​​pledging a lawsuit in Georgia to lead. Mr Herschmann said he replied that Mr Eastman was insane, adding that he told Mr Eastman, “I just want to hear two words from your mouth from now on: orderly transition.”

Mr. Herschmann said he went on to tell Mr. Eastman that he should get a great criminal defense attorney because he needed one.

The newly released email shows Mr. Eastman has not let up even after Mr. Biden was sworn in. It aired after the Trump campaign raised tens of millions of dollars from requests to Mr Trump’s supporters that suggested the money would be used to fight voter fraud, even if the allegations by Mr Trump and his allies were cleared by the courts dismissed and largely refuted even by Mr. Trump’s own Justice Department.

By suggesting using the Georgia runoff as a way to expose fraud in the general election held months ago, Mr. Eastman implicitly acknowledged that other, more direct, allegations of fraud did not gain traction.

The email suggests that Mr. Eastman viewed the Georgia courts as an investigative tool, using the investigative process to continue trying to substantiate previously dismissed claims.

“We must figure out how to keep the fight going,” wrote Mr. Eastman. “I’m inclined to pursue a challenge to the Georgia runoff, using what we’ve already learned (major statistical anomalies, violations of Georgian law, etc.) as a basis. According to Georgian law, any qualified voter can raise a challenge, even if the candidates themselves are not interested.”

In the email, Mr Eastman argued that if the group of lawyers and Trump advisers involved in the effort won in Georgia’s Jan. 5 runoff — those of Raphael Warnock and Jon Ossoff, both Democrats could uncover fraud, they could justify themselves for the claims they made about the November elections.

Towards the end of the email, Mr. Eastman hinted that the Trump campaign could fund the ongoing effort. He named a team of lawyers he would recommend, but said two of them would need to pay their outstanding Trump campaign bills before they would consider doing the work.

Mr. Eastman wasn’t the only one demanding payments from the campaign’s swollen coffers to help keep Mr. Trump in office. An employee of Mr. Giuliani sent an email to the campaign shortly after Election Day in 2020, demanding $20,000 a day in compensation for Mr. Giuliani. At the time, Mr Giuliani urged Mr Trump to keep fighting the election results and jumped at the opportunity to lead the legal effort doing just that.

But Mr. Trump told his advisors at the time that Mr. Giuliani would only be paid “on the come,” a reference to a wager in the casino game of craps, which is essentially a payment on a successful roll of the dice, according to two people with knowledge of the discussions.

Mr Eastman told some of Mr Trump’s assistants that he was working for free, according to one of those with knowledge of the discussions. At the same time, he had entered into a private arrangement with Bruce Marks, another attorney working on Mr. Trump’s efforts, to be compensated by Mr. Marks, although it does not appear he received any money that way.

When Mr. Biden became president, Mr. Eastman tried to get paid outright, the Jan. 20 email shows, though two people with knowledge of the campaign’s finances said he never was. In addition to trying to get paid for his time in the White House in January, he attempted to bill the Trump campaign $125,000 for his work on a lawsuit by the Texas attorney general attempting to tamper with the election results in a number of battlefield states to obtain invalid. The lawsuit was quickly dismissed by the Supreme Court.

Since the Capitol riot, Mr. Eastman has gone from a little-known conservative college professor to the best-known legal architect and promoter of the plan to use alleged lists of voters supporting Mr. Trump to try to block congressional certification or to delay Mr. Biden’s victory on January 6th.

His actions were the focus of both the Justice Department investigation and the House Committee investigating the Jan. 6 attack and its causes. Mr. Eastman repeatedly invoked his Fifth Amendment right against self-incrimination when questioned by the committee.

In face-to-face meetings at the White House in the days leading up to January 6, Mr Eastman tried to persuade Mr Pence and his top attorney Greg Jacob to go along with the plan to overturn the election.

At the first meeting on January 4, Mr. Trump and Mr. Eastman brought Mr. Pence and two of his best associates, Mr. Jacob and Marc Short, into the Oval Office. This meeting was followed by another on January 5, at which Mr. Eastman again attempted to persuade Mr. Jacob to go along with the plan.

After Mr Jacob refused, Mr Trump publicly pressured Mr Pence in front of a noisy crowd of his supporters at the Ellipse on January 6. Later that day, when a pro-Trump mob attacked the Capitol, Mr. Jacob emailed Mr. Eastman blaming him for the violence.

In March, a federal judge ruled in a civil case that Mr. Eastman and Mr. Trump most likely committed crimes in pushing to overturn the election, including obstructing the work of Congress and conspiring to defraud the United States.

The actions taken by Mr. Trump and Mr. Eastman, the judge found, amounted to a “coup in search of a legal theory.”