Hello drcsuefl
That is the autocomplete list - addresses are added as you send mail. You can get the autocomplete list from the old computer and use it on the new one.
It's at C:\Users%username%\AppData\Local\Microsoft\Outlook\RoamCache - it should be the largest Stream_Autocomplete_0_*.dat - and would have a recent modified date.
Copy it to same folder on the new computer. Close Outlook. If you have more than one email account in your profile, you may have than one autocomplete file - select the largest one. Press F2 or right click on the original and click Rename. Copy the name to the clipboard then add -old to it. Select the one from the old computer, press F2 or right-click and edit - paste the file name from the clipboard.
Restart Outlook. Most of the time, you will have the autocomplete list back. Occasionally it doesn't work - repeat the steps. If it fails the second time, you will need to build the autocomplete list as you go as it is corrupt.
-- Diane