What license did you get the A320 rating on?
To add the SIC rating on to a FAA certificate, you have to go to a FAA office in person and show them your training records and you have to have a 8710 form filled out and signed by your trainer. The requirements are found in FAR 61.55 (d). The training records have to be signed off in a certain way,
“[Applicant's Name and Pilot Certificate Number] has demonstrated the skill and knowledge required for the safe operation of the [Type of Aircraft], relevant to the duties and responsibilities of a second in command.”
I would call the training center and ask them if they have prepared paperwork for a FAA SIC type rating before, they should know what is needed if they have.