Complaint sub-issue: Attempted to collect wrong amount

I received a letter from FMS notifying me my account had been given to them for collections. I called them to discuss payment options and came to a compromise agreement. I agreed to pay the compromise amount and was told it would be expedited and take a couple of days to clear with the Department of Education. I informed them I would be mailing the check so it would give enough time for the compromise to clear. 
Several days later I got a call from FMS asking if I was going to pay the compromise amount. I told them that yes, as we discussed previously, I had already mailed the check. 
A week and a half later, FMS called again to ask if I intended to pay the compromise amount. I told them that I had sent the check over two weeks ago and that the payment should have been received by then. They needed some time to look into it and said they would call back. Later that day, they called back confirming that the check had been received, there was nothing more I needed to do and that my account would be closing out. 
A month later, FMS called me requesting I make a payment on my account. I informed them that I had paid a compromise amount and that my account should be closed. The representative confirmed that my account was closed. I then requested documentation of my payment and account closure. 
I did not receive any documentation or communication from FMS. I was sent a letter from Department of Education four months later informing me that my account was in default and was being referred to the Department of Treasury for offset collections. 
I then called FMS.The FMS representative I spoke with confirmed I had completed all necessary steps to comply with the compromise agreement and that my account should be closed. She then referred the account to a manager- XXXX XXXX . 
In my first conversation with XXXX XXXX, he told me the account was not closed out because the payment had posted the day before the compromise agreement was approved by the Department of Education. He informed me he would be submitting to them a recommendation to close my account and that he would call me back with an update within 48 hours. 
After calling him twice and leaving two messages, XXXX XXXX returned my calls more than 330 hours after our first conversation. In our second conversation, he told me that I was at fault for paying the compromise amount too early. When asked why the approval was not expedited, he claimed I did not notify FMS of my intent to pay until XXXX XXXX ( this is false ). He also claimed the Department of Education was not recognizing the agreement ( false ) and FMS had submitted XXXX recommendations to close my account and were waiting for a response ( no record of these recommendations with Dep of Ed ). 
I then called the Department of Education and spoke with representative XXXX XXXX. He confirmed the compromise date and that I had paid before the deadline. He stated that Department of Education relies on the collections agency for closeout documentation to initiate the closure of an account. He stated that Department of Education never received this documentation and he does n't understand why FMS would not have sent it. He also stated that he did not see any record from FMS recommending to close my account. He then initiated the closeout process himself and said I should receive documentation in 7-10 days. 
A conversation with another Dep of Ed represantative stated that paying a day early would not negate the compromise agreement as XXXX XXXX had claimed. 
I have copies of written communications, call logs, and phone recordings to verify information stated in this letter. 
I believe FMS at least encountered a clerical error in their system and rather than taking responsibility, lied and blamed me for the account staying open. At most, FMS attempted to defraud me to collect more money from managing my account.