The phrase "when they admit" is correct and usable in written English.
It is used to indicate that something happens after someone acknowledges something. For example, "He will be able to move forward when they admit their mistake."
People have been stoned to death when they admit they have AIDS.
And birthdays are thing people celebrate when they admit that they've aged".
RIO DE JANEIRO — While the U.S. Supreme Court considers whether American universities should take account of race when they admit new students, Brazil is implementing what are arguably the most radical affirmative action measures for universities in the West.
Reprieve's director, Clive Stafford Smith, said: "All politicians should be congratulated when they admit a mistake, and it is a credit to Vince Cable that he has backed down".
"People are often surprised to learn that when they admit the mistake, not only do they feel better, but the response is often much better than they expected," she said.
In May 1863, the Charleston Mercury captured the popular mood, supporting the idea of announcing to the world that "we will admit their Consuls when they admit ours; that we will respect the rights of their nationality so soon as they respect ours; that we will acknowledge their citizens to be their citizens just when they acknowledge us to be citizens of the Confederate States, and not till then".
Senior management came under widespread criticism in September when they admitted that nearly six million people had been charged the wrong amount of tax.
In November tax officials dented the government's data-security credentials when they admitted losing the personal details of 25m benefit claimants.
But this week US forces were criticised when they admitted using white phosphorus during the 2004 assault on Falluja to flush enemy forces from well-covered positions.
But in fall 2004, Greek officials stunned European policy makers when they admitted that the country's budget deficit had exceeded the European Union's ceiling of 3 percent of gross domestic product in every year since 1997.
(The defendants in Regina v Dudley and Stephens were found guilty when they admitted that they actually murdered the child they ate, but trust a defense team to put a different spin on it).
