Ok it looks as if this is not money owed to a government body but a company. If so the FOI would not be relevant.
if it went to court and they won, my initial focus would not be on, if or when the letter was sent.
If it went to court the company should have provided the court with suficient documents to satisfy the judge that the debt was owed or at least that there was no defence submitted against the debt.
But that is the documentation you should look to obtain as that is what the court ruled on when deciding the money was owed.
Your only option to remove the court order would be to go back to court for that you would be best served by getting legal advice.
You could check if you have insurance cover which provides an advise line or try posting on a debt managemet website or contact a debt managemet charity.
The first item to reopen the case can be proving that proper notice was given, which is what I am going to assume is the disputed letter?
There is a question on how the debt happened.
Some contracts can bind your relative's estate after death so depending on details on how and when the debt happened. There would also be a question around the passage of time between the death and the reliance on the contractual obligation to pay the "new" debt.
If the estate has been paid out and there is no money left the issue becomes can the court judgement be transferred to the people who settled the estate.
Depending on the amount of the debt and the ethics of the people involved getting the court documents may be faster and once you have that, you can decide if you need to contact a legal adviser