MailStore can be accessed via a web interface at the following - MailStore Web Access
Following that link will bring you to a log in page, your login will be your First name and last name as one word i.e. JohnSmith and your usual server/email login password.
Once logged in, the left side of the page will show yours and any assigned email archives, displaying your incoming and outgoing mail, if the mail is older than 2021, you may have an "Exchange" folder, this will display these older emails:
To search the MailStore webapp, just click the search bar at the top left of the page, this will also allow you to choose parameters to narrow down your search: 
You can also save any emails by clicking "Open as...", and can be saved either as an EML or MSG file, select the file type from the drop down and click the "Open as" button to download a copy.
