On a stage Friday at Georgetown University, Hillary Rodham Clinton, John Kerry and Laura Bush were taking turns begging Americans not to abandon the women and girls of Afghanistan after the last U.S. troops come home next year.

Briefly, a Kabul classroom filled with beaming young Afghan women at the American University there got to see their famous champions and non-famous counterparts — including about 700 Georgetown students — through a satellite hookup.

They waved, and then we waved, and then they waved, and then someone in Kabul yanked the last grinning, waving girl’s arm down. At that point, the camera was turned off and the live image of excited women in hijabs that had been projected onto a large screen at the front of Gaston Hall was replaced with a still photograph of a young girl raising her hand in class.

The optics of the abruptly cut link were unfortunate: We can’t see you, so now we can concentrate better on the message of how we shouldn’t lose sight of you? But it was a perfect representation of the challenges all of the speakers described.

Bush, with great feeling, said she feared that “once the troops leave, American eyes will move away” from Afghanistan.

To a shameful extent, they already have.

But “I’m so worried” they’ll think we’ve forgotten them again, Bush went on. “I want the people of Afghanistan to know the people of America are with them.’’

“I agree completely with Laura’s comments,’’ said Clinton. “The number-one issue on the minds of Afghani women is how can they continue their work if they don’t have security” after U.S. troops leave.

The questions Bush and Clinton heard from the girls in Kabul focused on security, too: How could they continue to raise awareness about women’s rights and protect the gains they’ve made without Americans there to protect them?

Both former first ladies said Americans would have to find ways to continue supporting them — through exchange programs, raising money and donating to groups already on the ground there.

Bush said she knew that Afghan women would continue to get the word out that they won’t allow the clock to be turned back. Clinton advised them to get involved in next year’s elections.

But they also have to hope that their government signs off on a security agreement with the United States in the next two weeks, Clinton said, so that America can continue to support them on the ground. And that won’t happen, she said, unless Afghanistan agrees to extend immunity from prosecution to American personnel.

Anita Haidary, a young Afghan woman attending Mount Holyoke College in Massachusetts, talked about returning to her country after spending 11th grade in California. She started an anti-harassment group — made up of male and female friends — that went out on the streets to confront men who harassed women. “We are not stuck in the past, but we need your help.”

Decades of war in her country have left deep wounds, Kerry said in his prepared remarks, and discrimination and domestic violence against women “continue to be major problems.”

He told the story of a female police officer whom his team met recently in Kabul. She had heard screaming coming from a house she was passing on her way home from work. Kerry said she broke down the door, found the man who’d been beating his wife standing over her and took the woman home with her to take her statement. He didn’t say whether the husband was arrested.

But “it would be more than a tragedy to let women slip back” from all the advances made in education, health and economic independence in the dozen years since the Taliban fell, Kerry said. Female life expectancy is at 64 years, up from 44, and in the past five years, 120,000 women have graduated from high school. About 40,000 are in college now.

If he could ask only one question before walking into any area in Afghanistan, the one that would tell him the most about the overall security and stability in the country is “What percentage of local girls are in school?”

In case any of the Afghan students we briefly glimpsed caught sight of anyone in the heavily female crowd of Georgetown students dozing, here’s why:

“We’ve been here since 3 in the morning’’ to get a ticket, said Laura Lannon, a freshman from Chicago. Anyone who showed up after 5 a.m. didn’t get in. Lannon said she was there because she loves Clinton so much, but she found that she most appreciated “seeing Hillary and Laura together, because of all the disagreement in Congress now, I was happy to see that.”

Several students said they found their contemporary from Mount Holyoke the most moving of all the speakers — “motivational,’’ one said. It was after noon before they walked out of the school’s main building, where they’d been waiting since well before dawn. “Good night!” they called to one another as they headed home in the midday sunshine.