Product: Credit reporting, credit repair services, or other personal consumer reports

The debt collector ( XXXX ) has falsely " parked '' old debt on to my credit report that was found to part of identity theft from XX/XX/XXXX. They have tried to " reage '' this debt onto my credit report as being opened XX/XX/XXXX and owing {$1200.00}. They have also falsely and illegally reported twice on this same account for another {$1200.00}, and have falsely said this was opened XX/XX/XXXX. Equifax continues to allow them to report twice on the same account despite several attempts to explain what has happened. It is clear on my credit report that XXXX has reported falsely twice on the same account. I am calling into question Equifax investigation into my accounts. I have explained that this account was fraudulent and has been removed from my credit report several years ago. 
It has now " reappeared '' on my account as an attempt to ruin my credit profile and collect a debt that is not mine. I have asked Equifax what information they have received that is proof that it is my account and they have told me over the phone that XXXX XXXX XXXX says its my accounts and that they have confirmed that I owe the amounts. So I asked them if they just take their word on it or actually receive proof. 
Their response was that XXXX responded that I owed the money. I have an issue with Equifax reporting on two of the same accounts because in their words " have different account numbers ''. These new account numbers are made up and one account is named " XXXX '' as if this account is new. XXXX recovery services has illegally harmed my credit on a debt that is not mine. XXXX and XXXX cleared this identity theft over 3 or 4 years ago. I have written XXXX with no response. I have asked them to remove this from my debt as I do not owe on this debt. I have also asked Equifax to properly gain proof this is my account, which they have not done. Not only has XXXX refused to give me information on this debt, they have now double reported on my credit report in an effort to collect more money from me. Equifax has allowed them to do so. XX/XX/XXXX and XX/XX/XXXX has cleared this up over 3 years ago. My next step is to sue them in court if this is not resolved. I have attempted to get this fixed for almost 2 years now with XXXX and Equifax. They have falsely reported wrong information on my credit report with Equifax, with the sole purpose of keeping this debt " alive '', when it should have been removed from statue of limitations in XX/XX/XXXX and when this was found to be used from identity theft years ago. Because this information was removed over 3 years ago from my credit report I did not keep that paperwork as I thought it was final and I have since moved several times. The original debtor was XXXX and had been removed from my credit report only for them to sell this wrongful debt to XXXX after it had been found to be part of several accounts used as part of identity theft. I have asked for any signatures of mine, driver license, proof that this was my account and have yet to receive anything back. Please help me get this matter resolved as I feel extorted to pay two debts on an otherwise clean credit profile while Im looking to purchase a home. After an inquiry on a mortgage is when the 2nd reporting of the {$1200.00} debt was added to my credit report. Equifax investigation practices should require proof that both of these are my accounts and shold have been able to see that the 2nd account was a duplicate account for the same exact amount and removed it immediately. Thank you for your assistance.