Hi. What is your first name? I don't have a record of your email address on our membership file.
To your query...
Assuming that you have Office 2013 or later, I would suggest moving the emails that you want to keep to a new
Outlook Data File (.pst) as described here
https://support.office.com/en-us/article/Create-an-Outlook-Data-File-pst-to-save-your-information-24e6eafe-5700-4994-99e6-1783f556bbd2 Then you can open this file in Outlook to see your messages, regardless of your Telstra account. I would also suggest making a backup of this new PST file on a USB disk since it is held locally on your hard disk in your Documents > Outlook Files folder, not in the cloud.
Then I suggest that you keep adding messages that you want to keep to this new PST file until you get switched over to the new Telstra mail
Meanwhile, set up a new account in Outlook with the new Telstra Mail settings so it is ready to operate when the changeover occurs (unfortunately you won't be able to test it until that time).
When you are satisfied that the new account is operating after the changeover, and you have saved messages from the old account to the above PST file, then you can delete the old account.
Have fun
John