Finfisher is legitimate surveillance software thought to be used by governments to covertly obtain data.
It is installed unknowingly by its target computer user, often by disguising itself as an update to a well known programme such as Firefox.
Gamma International has not responded to emailed requests for comment.
University of Toronto research group The Citizen Lab said it believed Finfisher command and control servers were currently active, or had been present, in numerous countries.
In 2011 the BBC found documents in the state security building in Egypt, looted during the uprising, which suggested that the Hampshire-based firm had offered to supply Finfisher to the Egyptian government to monitor activists.
Gamma denied supplying it but the files seen by the BBC described a five month trial which included successful access to email accounts and the recording of encrypted Skype calls.
Mozilla has now sent a cease and desist letter, warning Gamma not to use the name of Firefox, its browser, as camouflage for the program.
"Our brand and trademarks are used by the spyware as a method to avoid detection and deletion," said Mozilla chief privacy officer Alex Fowler in a statement.
"AS an open source project trusted by hundreds of millions of people around the world, defending Mozilla's trademarks from this abuse is vital to our brand, mission and continued success."