This probably wont help a lot other than for my reference to a very useful tool you can get from Nirsoft for free called the nk2 reader. The answer above is true for Outlook 2007 but if oUTLOOK 2010 is involved anywhere, everythng is different.
I recently had to do this with about 40 systems some 2007 some 2010 and it took me a while to find it but the name of the file you want in Outlook 2010 is "stream_autocomplete.......". It is located similar to where the old nk2 file was and is a hidden file you have to enable seeing hidden files and folders first in control panel.
Then go to “Username”/appdata/local/Microsoft/Outlook> RoamCache. However, getting the "stream" file from one computer to another is nowhere as easy as it used to be with an NK2 file. Microsoft has some information on their site about it if you search for "stream_autocomplete".
But by far, the best help you will find is a tool made by Nirsoft called the nk2viewer which you can get for free from their site. It works on both the old Nk2 files as well as the "Stream" files and appears to allow you to open in one format and save in the other.
Word of warning. The user’s identity is in the numeric string at the end of the "stream_autocomplete" filename and even if it is the same user on a different system they will have a different ending.
One method I found suggested that seems to work well is to send one email with their new account on the new system. Then close Outlook and go to the location I gave above Find the “stream_autocomplete” file (it will be very small maybe 1 kb)
Copy the OLD “stream autocomplete” from their old system into the same folder (It will be a lot larger). Then use rename to only change the numeric endings. You will want to copy all the string after "stream_autocomplete" onto notepad or somewhere you can see it (just to be safe), then delete that whole file and use the data you saved to rename the OLD autocomplete so that it has the Identity string of the one you just deleted.
Nirsoft nk2reader makes this a lot easier and additionally allows you to see the names inside the file and a lot of other data.
I should add that I have recently had to make much use of this solving the same problems as you are and there are other factors involved as well. Such as the number of names in the autocomplete. There is a limit. If the list is too long, it often doesn't get read at all so you end up with nothing. However, by using the same tool I listed, you can delete names that you no longer need in the autocomplete making it small enough to work again.
Another method which appears to work is to go to the old copy of outlook on the other system, copy all the names you will find in either contacts or suggested contacts (Be careful to only copy email addresses, use list view or some other but do not get the addresses and phone numbers mixed in) paste the list of email addresses into an email body, send that email to the user on their new system. Once you open it, copy the names from the body of email. Start a NEW email and paste the names into the TO: or CC: field (I have been told either works, even BCC: ). You DO NOT send the email to all those people, instead click FILE and SAVE. Then just close the email.
I wish you luck as I have just had to do over 40 systems with this same issue and spent many hours finding the information here. The worst part is that there did not seem to be any one method that always worked for everybody. In some, the File/Save worked perfectly and was very easy. In others, the nk2reader tool worked best. In in still others renaming the stream file seemed to be the solution.
It depends on how many you have as to how much trouble it is worth to get the results. In one case, my only option was to use an email address extractor on their “sent” folder.
The common thought was that “Suggested Contacts” was the new autocomplete list but this is not true even though it may be a close match and would certainly be the best place to go to get a mailing list from. In Office 2013 MS has decided to complete do away with the “Suggested Contacts” list due to this misconception. They say that the Stream Autocomplete is actually an “integral part” of the PST and unless you are going from Outlook 2007 to Outlook 2010 simply importing the old PST into the new PST should carry forward many of the settings from their old Outlook into the new. But.. if your old version is 2007, then you definitely want to import the old PST into the new PST due to differences in file structure.
While I don’t advise this last possibility as it could bring problems of its own, If BOTH the Old and the New are Outlook 2010 and have the exact same username, and all the mailbox settings for email are identical, you can go ahead and setup the new copy to create the new PST, then drop the old PST into the Outlook Files folder in My Documents. If everything is the same, then the PST file will also have the same name. (email@example.com). If you tell the old one to overwrite the new one, I have done that a couple of times and it did seem to work. When you open Outlook afterward you will find everything in the correct folders and so on. I would consider this a Last Choice for emergency only option!
Anything with Outlook is always a challenge!