It is unclear as to how a showing of when you moved will determine whether or not you have a legitimate debt with ConEd.
The issue is whether or not, when you terminated service, there was any amount due.
Hence, the basis for the earlier question as to when the account would have become delinquent as opposed to when the debt collector opened their collection.
The date of your first delinquency establishes when any collection, regardless of any other date such as date opened of the collection, must become excluded from your credit report. The DOFD is apparently in 2012, which will result in a likely exclusion sometime in 2019.
What is showing in your credit report as the reported DOFD?
If your new dispute challenges the accuracy of the reported DOFD as opposed to the legitimacy of the debt, then it would be a new dispute.
Documentation to support a dispute of the DOFD would relate to a showing of when you would first have become delinquent, which would likely be approx a month after your termination of service.
When a debt collector reports a collection, they are required to separately and specifically report the DOFD to the CRA no later than 90 days after they report their collection.
The CRA does not speculate or determine the DOFD based on any other information reported to them. It thus must be of record in your credit file. See FCRA 623(a)(5).
If your commercial credit report does not show the DOFD (which is common), you can get a report from annualcreditreport.com, which will usually show the reported DOFD.
You then have a date upon which to base any dispute of its accuracy.
Personally, I would provide documentation of when you sent notice to the utility of termination of service rather than simply sending documentation of when you moved.
It is possible that a consumer could move and yet not terminate service, such as if they are still the owner and are thereafter renting to another.
Documentation will depend upon the facts of your individual case, and should relate as closely as possible to actual termination of your service agreement.
When you dispute the accuracy of reported information, the CRA forwards a copy to the furnisher, and the furnisher must conduct a reasonable investigation and report their finding back to the CRA. They are not required to "prove" the accuracy, or support their finding with documentary evidence. There also is no appeal process to contest the finding in a dispute. However, you can file another dispute if it is not "substantially the same" as a prior dispute. A second dispute is not substantially the same as a prior dispute if it includes substantive new information pertinent to the dispute. Otherwise, the finding concludes the dispute process.
If you disagree with the finding, you can then obtain a full legal review, including obtaining discovery of any pertient evidence, by filing a civil action and getting the matter before a court.