Click on File, New, Outlook Data File. Make sure the type of storage is set to "Office Outlook Personal Folders File (.pst)" and click Ok. Select the folder where you want to store the file and change the name if you don't like the default then click Ok. In the next dialog just click Ok.
The folder list should now be updated. You will see a new item, "Personal Folders", at the bottom. Right click on it to create a new folder. The dialog that appears will allow you to select the type of items you want to store in this folder. The default is Mail and Post items which is fine if all you want is emails. Give the folder a name and click Ok. Depending on what your FIL wants transferred you may need to create several folders, e.g. one for his inbox, another for his sent items and so on.
To copy all the emails from the inbox to a folder in Personal Folders go to the inbox, type CTRL+A to select all emails then CTRL+C to copy them, go to the destination folder and type CTRL+V.
Once you've copied everything you need right click on Personal Folders and select Close "Personal Folders". You will then need to close Outlook down before you try to copy the file.
You are now ready to copy the file to the new PC. Once it is there and you have Outlook running select File, Open, Outlook Data File and select the file you have copied. The folder list will now include "Personal Folders" and you can copy the emails to their final destination.
Hope this helps.