You can move a contact if they have left their current business, by clicking on the Move Contact icon. Once you click on the icon you will be prompted to search for the name of the business to move the contact to. Once the new business is located, select the name of the individual and click OK. The contact will be moved to the new business; the history, activities, and documents will stay with the current business.
If you select a contact to move and the contact is currently linked to the Account and has Reporting Requirements you will be prompted to ask if you would like to remove the links?
Select the Account Links and Reports to remove and click Next.
Search for the Business to move the contact to and click OK to finish moving the Contact.
Note
Moving a contact is discussed from 1:10-1:50 in the below video.