Once a Lead has been changed into a Customer, it will disappear from the 'Leads' list and show up in the 'Customers' list. (Customers may be called something else (like 'Submissions' or 'People') depending on your instance customization.)
See the screen recording provided below (click the link) to get a visual explanation of converting a Lead by changing the status one of two ways.
(Leads can also be converted from within the FastGem overlay tool, by changing the work flow status to a passing status from the overlay when accessing a provider portal. For more information on using the FastGem overlay tool, see the article "Accessing and Utilizing Overlay Tools.")