Export one to a PST file. Copy the PST file onto the second computer. Access the PST file from Outlook and copy all of the files from the PST file to your inbox.
You can also take the exported pst from the other computer and import it into outlook on the second computer. Go to file – import and export. Find the exported pst on the cd or thumb drive you copied it to, and import. Saves you from copying all that mail!