I once dated a man who claimed to have flashbacks and PTSD from being a macv-sog special forces sniper disguised as a photographer. His 'service' was all made up. Eventually I found newspaper photographs he had taken regularly during the time he was supposedly in Vietnam and showed them to him on an internet archive. He claimed that was another person in the same town with the same name but he never admitted faking flashbacks to places he never was.

So yes it is possible to fake mental illness.