GEORGETOWN, Guyana — When Officer Randolph Holder forgot to call his grandmother here, she fretted. She would go to a neighborhood Internet cafe to check up on him, only to hear him wave away her worries from the other end of her cheap online connection. He would lament only that he could not arrange his clothes as neatly as his grandmother did.

The call that the grandmother, Elizabeth Lovell, got on Tuesday night was far graver. Her grandson, a widely respected New York Police Department officer who followed three relatives into law enforcement work, had been shot in the head and killed on the job in East Harlem.

The visit he had planned to his home country this Christmas was no more, the fish his grandmother looked forward to frying for him no longer a concern. The cash gifts for her birthday and Mother’s Day would end, and the promises Officer Randolph had made to bring a little brother to the United States would fade.

“I could have died,” Ms. Lovell said on Wednesday, clutching a photo of her grandson in uniform. “The phone fell out of my hands, and I had to go sit in a corner. I felt weak, weak, weak. Like I didn’t know what to do.”