Should we keep track of an employee’s disability payments even after he’s left the company?

Q: “We had an employee who went on long-term disability before his employment was terminated, which happened in February 2015. He is still receiving long-term disability payments. Should we be maintaining a copy of the documentation of his payments? He is no longer an employee, but if he files for unemployment compensation once his disability payments stop, will we need that documentation?” – Joanne, Oklahoma