A California man was convicted on Tuesday of cyberstalking and threatening to kidnap relatives of those killed in the 2018 mass shooting at Marjory Stoneman Douglas High School in Parkland, Fla., federal prosecutors said.

The man, Brandon Michael Fleury, was found guilty of three counts of cyberstalking and one count of transmitting a kidnapping threat, according to Ariana Fajardo Orshan, the United States attorney for the Southern District of Florida. Mr. Fleury, 22, will face a maximum possible sentence of 20 years in prison when he is sentenced on Dec. 2, prosecutors said.

Over the course of three weeks, from late December 2018 into early January 2019, Mr. Fleury used 13 different Instagram accounts to target survivors and victims’ loved ones, prosecutors said. He operated under various aliases, including Nikolas Cruz, the man who has confessed to killing 17 people at Stoneman Douglas, and Ted Bundy, the notorious serial killer, according to prosecutors.

From his home in Santa Ana, Calif., Mr. Fleury sent dozens of messages using Instagram handles that included “the.douglas.shooter,” “nikolas.killed.your.sister" and “nikolas.the.murderer,” and images of Mr. Cruz as the accounts’ profile pictures, according to court documents.