Police identified Beauchamp as a suspect Monday night through a previous arrest in connection with an Occupy Wall Street protest on Oct. 8, 2011, according to police sources.
The argument between Beauchamp and Basin, of Howard Beach, began as a verbal dispute while the two men were riding the Manhattan-bound L train Friday.
Both men exited the train at the Bedford Avenue station, where police and witnesses say the fight turned physical.
They fell into the train tracks. Beauchamp was able to get back to the platform, but Basin could not get off the tracks, according to police. He was struck by an oncoming L train.
He was transported to Bellevue Hospital and was later pronounced dead.
Basin was a student at LaGuardia Community College in Long Island City studying psychology.
"My son was very friendly," Basin's mother Zena told NBC New York. "He would never hurt anybody, if you ask any of his friends, they knew that he would go out of his way to help them."
Get the latest from NBC 4 New York anytime, anywhere. Follow us on Twitter, Facebook and Google+. Sign up for email newsletters here. Get breaking news delivered right to your phone -- just text NYBREAKING to 639710. For more info, text HELP. To end, text STOP. Message and data rates may apply.