Is collection finally closed?

I had a collection that I paid off years ago. Suddenly I got a letter from a lawyers office representing Pinnacle Credit Services LLC. They were trying to claim this old debt once again. I sent a certified letter to the law office and the collection agency to verify debt, and threaten suit if they did not correct records etc. The law office sent me a reply that the account had been closed and placed on cease and desist status. Can I consider this enough evidence that I am in the right and the account is truly closed to future collections on it?