It depends on the age of his previous cert. From the Jeffco site:
"A training certificate from a handgun training class obtained within 10 years before submitting this application. The certificate must include the original signature of the certified instructor who taught the class.
A “handgun training class” means: a law enforcement training firearms safety course; a firearms safety course offered by a law enforcement agency, an institution of higher education, a public or private institution or organization or firearms training school that is open to the general public and is taught by a certified instructor; or a firearms safety course or class offered and taught by a certified instructor.
A “certified instructor” is a firearms safety course instructor certified by a county, municipal, state or federal law enforcement agency; the Colorado Peace Officer Standards Training (POST) board; a federal military agency; or a national nonprofit organization that certifies firearms instructors, operates national firearms competitions and provides training, including courses in personal protection, in small arms safety, use and marksmanship."