Yes, however you can only transfer 9 credit hours of coursework taken prior to entering a graduate program. The Certificate is considered a Second Bachelors. You cannot actually just "transfer" to the graduate program; you must apply with all other applicants by the annual posted deadlines in December. Be aware of the additional application requirements for a graduate program that differs from the Certificate. You must take the GRE, for example, and have a written Statement of Purpose to outline your research objectives.
Applicants are considered as qualified to study in the program they apply to. However, you can apply for the Ph.D. internally with their GRE scores in December. In the spring (May), you would need to sit for the Oral Comprehensive exam in addition to the Written Comprehensive exam.
If I already have a Master's degree, do I still need to submit a GRE test result if I am applying to your Master's or Ph.D. program?
If you took the GRE for your first Master's degree, you will not need to retake it. Please submit your scores from the last exam, even if it was more than 5 years ago. If you were not required to take the GRE for the first degree, you will need to take it to apply to this program. Some programs may emphasize excellence in different areas of the GRE than we do, so we would like to see your scores regardless of whether you have already earned a Master's degree. However, if you have a PhD, we do not require your GRE results.
I do not currently have a graduate degree but took the GRE 8 years ago. ETS does not keep them more than 5 years so I cannot have them send you my scores. Do I need to retake the GRE?