“That job is not finished and we are committed to sharing our progress,” Facebook said in a statement.

Kim Joiner, a deputy assistant to the secretary of defense who oversees the military’s social media accounts, said her team works with Facebook to remove impostors and was pleased with the company’s response. “I’m absolutely satisfied,” she said.

When shown that searches by The Times for three top American generals on Facebook and Instagram had yielded more than 120 impersonators, Ms. Joiner said it was “disturbing.” She said she did not know why the fakes were not eradicated.

“I mean, the numbers are astounding,” she said.

‘My wife’

To her friends and family, Ms. Holland was known as trusting and impulsive. Born in Philadelphia, she had spent time in Arizona and Missouri, working as a gardener and in an auto shop. She met her fifth husband, Mark Holland, when she offered him a ride off the side of the road.

In 2001, she moved to Delaware to care for her sick mother. When her mother died in September 2016, Ms. Holland found herself depressed and with free time. She noticed her sister glued to her smartphone, scrolling through Facebook. So she bought a smartphone, too, and created a Facebook profile.

A few weeks later, Ms. Holland got a Facebook message from a stranger. The profile showed a man in uniform named Michael Chris. He told her he disarmed bombs in Iraq.

Image A selfie of Mr. Anonsen that impostor accounts used on Facebook and Instagram. Credit...

Ms. Holland said she initially felt uneasy, but the conversation flowed. Mr. Chris told her about life at war. She made him laugh.