If you wish to view the customer's purchase history, you must first set the customer in Cloud POS.
Once the customer is set, you will see the value of the customer's purchases to date in the transaction summary panel:

If you would like to view further information, you can view a full Purchase History section in the customer's record in the Back Office. There is a link to this page in the Customers menu:

Alternatively, you can click the Edit pencil icon next to the customer's name in the transaction summary panel.

This will open the Edit Customer Details screen. At the bottom of this screen, click the View Customer Card button. This will also open the customer's full record in the Back Office.

On the Customer Card, click the Purchase History tab at the top:

You'll then see a list of the customer's previous purchases. It's grouped by transaction by default, and you can use the filters in each column to narrow the results down to a particular transaction, date, ILC, description, brand etc.
