I recommend getting that in writing, and not just over the phone.

You could do that by writing to thank them for the information given to you over the phone, and setting out your understanding of each steps you need to take to close things off properly, and asking that they please confirm that it is so, and add any other info you may need to know.

The reason for this caution is that, over the years, we've seen countless people think that they'd understood that x or y was okay, or really having been told so by the person over the phone, but then, when the real steps needed to be taken, it was not exactly as they'd been told, or had understood.