Product: Credit card or prepaid card

I am writing his letter in hopes that you could help with the abusive and fraudulent practices of Citibank/ Sears Department store credit card. 
In XXXX of XXXX, a Sears card was opened without my knowledge, consent, or permission. Since then, my credit has been destroyed by a delinquent account that I did not know existed. For months, Sears was sending statements with my name on it. Since I did not have an account with them, I immediately discarded the envelopes as junk mail. My wife eventually opened a letter and observed we were days from going to collectionon an account that I never opened. 
I attempted to resolve the matter by calling their customer support line. They transferred me to their fraud department and assured me the matter would be resolved. Approximately 1 month later, I received a letter stating that my claims were unfounded and I would be responsible for the charges. I was furious because nobody from their fraud department called to actually take my statement. They just went off the few questions asked by the customer service representative. To make matters worse, late charges continued to compound during their investigation. 
I spent the next 3 consecutive days ( about 1.5 hours PER DAY ) on the phone with the customer service line trying to clear this matter. I spoke to the fraud department and requested to speak to an investigator. They opened a new fraud claim and assured me I will speak to an investigator. Unwilling to allow my credit to be further destroyed, I asked to pay my account off in full. She indicated I owed approximately {$250.00}, but stated she could remove some late fees. An agreement was made that if I pay {$11.00}, my balance would be paid in full and my account would be closed. Both parties clearly understood that I still intend to dispute the accounts legitimacy, but I was only making the payment to stop the harm thats being done to my credit. On XX/XX/XXXX, I paid {$110.00} and was told my balance was paid in full. 
Approximately 1 month later, I receive a statement indicating an {$80.00} balance was 2 months delinquent. From this point on, all conversations were recorded on my end with their knowledge and consent. I spent the next 5 consecutive days to customer service that offered absolutely no help. Every single call ended the exact same way. After 1.5-2 hours, I was informed that they were unable to help me at their level. They attempted to transfer me to management, but nobody answered. They took my information and assured me I would receive a call within 24 hours. Nobody ever called me. My final conversation on XX/XX/XXXX ended with a promise that I would receive a call from the fraud department within 24 hours. The call never happened. Once again, I paid over {$45.00} to stop my credit from being harmed with the understanding that my balance is paid in full and I may still dispute the legitimacy of this account. 
On XX/XX/XXXX, a letter was sent stating my I am responsible for the charges for the following reason : You had knowledge of this debt and your actions indicate the same when you failed to call or question the resulting account of charges. 
My knowledge of this account is only due to the 25 letters received in the mail!

There are two matters I am requesting your assistance : 1 ) I  am disputing the legality of this account. I am requesting a full reimbursement of all money paid into the account, and a reversal of any damage done to my credit rating. I assure you they will be unable to provide any credit application with my signature on it. I never gave them my information, nor have I given permission to open a Sears card on XX/XX/XXXX. 
2 ) Read the transcripts and listen to the recording on XX/XX/XXXX when I was assured that {$110.00} would pay the balance in full and my account would be closed. After this agreement, how is it legal to tack on another {$80.00}? 
I have very good credit and always pay my bills. This company is so frustrating. Ive spent over 40 hours on the phone and have never spoken to anyone who has the power to help. Any assistance would be greatly appreciated. Thanks so much for your time.