After you migrate to your new Office 365 Exchange Online account, you are able to add any archived email you had from your UW Bothell account. Below you will find the intructions on how to add your archived email to your Outlook 2013.
1) Open Outlook 2013/2016 and click on the "File" button in the upper left-hand corner.
2) In the "Open & Export" section, click on "Open Outlook Data File".
3) Click on the .pst file that you wish to import, then click on "Open".
4) The archive folder will now appear on the left-hand pane in Outlook, and your old archived emails will be in here.