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Sounds like ID Theft I would follow these prcedures to have it removed if they do not do so in a reasonable amount of time
What you requested is debt validation by the debt collector.
A DV request imposes an automatic cease collection bar if it is timely submitted, which is what they have apparently now acknowledged.
A DV request must technically be submitted in writing in order to impose any requirment. See FDCPA 809(a).
However, notwithstanding the requirement to submit in writing, the debt collector has apparently decided to accept the request, and as informed you as such.
A timely DV has now placed their collection activities on hold until such time as they decide to send validation.
There is no time period in which they must reply, and in fact, no requirement that they reply at all. As long as they continue to cease collection activities, they are in compliance with the DV process. You are thus under a state of limbo.
A DV additionally does not impose any requirment to delete their prior reporting, so the collection can remain during the limbo period.
As suggested in another reply, you can also deal with the situation by other means, such as filing a police report and treating the asserted collection as an identity theft issue. If you follow the identity theft process set forth under FCRA 605B, then you can get the collection blocked from your credit report, provided you can make the sworn statement in a police report that you never authorized the asserted debt.