Here is some relevant information. I think you need to contact your previous sponsor/university to do the J1 program transfer from the previous university to the current sponsor/university. Then, this new university can issue a new Form DS-2019 to you.
Here is some relevant information:
http://exchanges.state.gov/jexchanges/visitors/change.html
Transfer
The transfer of a participant from one program (sponsor) to another may be allowed at the discretion of the responsible officers and must be within the same category. The responsible officer of the program to which the participant seeks to transfer is required to verify the participant's visa status and eligibility, to issue a new Form DS-2019 reflecting the transfer, and to obtain the release of the participant from the current responsible officer, who indicates approval of the transfer by completing and signing block 8 of the new Form DS-2019. Transfers are not permitted in all categories, and a transfer does not extend the maximum duration of the program. Participants should address all inquiries regarding change of category to the responsible officer of their programs. [22 CFR 62.42]
Here is some relevant information:
http://exchanges.state.gov/jexchanges/visitors/change.html
Transfer
The transfer of a participant from one program (sponsor) to another may be allowed at the discretion of the responsible officers and must be within the same category. The responsible officer of the program to which the participant seeks to transfer is required to verify the participant's visa status and eligibility, to issue a new Form DS-2019 reflecting the transfer, and to obtain the release of the participant from the current responsible officer, who indicates approval of the transfer by completing and signing block 8 of the new Form DS-2019. Transfers are not permitted in all categories, and a transfer does not extend the maximum duration of the program. Participants should address all inquiries regarding change of category to the responsible officer of their programs. [22 CFR 62.42]