Between the five foreign nationals are convictions of domestic violence, threatening a crime with intent to terrorize, drug possession, dealing drugs, obstructing a police officer, kidnapping, robbery, felon in possession of a firearm, and auto theft.
Brown earned the "Moonbeam" nickname when he was governor in 1970 and floated ideas for a California space academy and launching a satellite for emergency communications. Jerry Brown, who pardoned five ex-convicts this week in an effort to keep them from being deported.
Pheach, who was convicted in 2005 and sentenced to six months, came to the United States at the age of 1 from Cambodia. He served almost a year in jail and three years of probation.
Trump's rant appears to have come in response to a segment on Fox News, which he tagged in the tweet.
Trump's tweet criticizing Brown is "odd", Stock said, "because the president himself has exercised the pardon power".
Brown (pictured) pardoned these immigrants before the faced the possibility of deportation.
But Brown calls this lawsuit a "publicity stunt" by the administration as it continues to push Trump's "America First" agenda.
The three others pardoned who are facing deportation are Francisco Acevedo Alaniz, Daniel Maher and Sergio Mena.
Maher is now the recycling programme director of Ecology Centre, a non-profit based in Berkeley, California.
"Daniel's case is of a person who made one mistake as a young adult, served his time and then completely turned his life around", the centre said. Mena served three years of probation after being convicted of possessing illegal drugs in 2003.
Trump's criticism of the pardon power could remind the public that Trump has refused to rule out using it himself on key figures implicated in the ongoing Russian Federation probe.
Those pardoned Friday included Sokha Chhan and Phann Pheach, both of whom face deportation to Cambodia, a country ruled in the 1970s by the genocidal Khmer Rouge.