The late Oscar-nominated actor starred in futuristic movie The Age of Stupid, which focuses on a man looking back at footage of the world in 2008 and asking why more wasn't done to stop climate change.
The film, which was directed by Franny Armstrong, was shortlisted for the Impact Award, which honours films for their influence on society.
The Age of Stupid is in the running for the $72,000 (£44,000) cash prize, and is up against Burma VJ, The End of the Line, The Reckoning: The Battle for the International Criminal Court, and Trouble the Water.
Crash star Thandie Newton and documentary filmmaker Morgan Spurlock will help pick the winner, who will be announced at a London ceremony in October (11).
Postlethwaite died from pancreatic cancer in January (11).