You shouldn't fake your degree.
Greg has no post high school education and is applying for jobs with limited success so far.
Greg wants to update his resume to increase his chance of success at getting hired.
Greg writes on his resume about his current, up to date employment history.
Greg writes on his resume that he graduated from college at the top of his class.
Greg gets hired at a job that utilizes the skills he's learned while working, and is soon promoted.
Greg gets hired at a job he's completely unqualified for and is quickly fired.