Two suggestions
One.
In the mail options where the email is downloaded from the mail server the the email left on the server for 10 days or so. Have both Outlooks connect to the mail server and they will both download the same messages. Downside, each user will not know it the other viewed,responded etc..
Two
On one of the computers share the folder with the .pst files and on the other computer map the folder and link it in outlook. Downside both users cannot use the email at the same time.
HTH
Brian