The access to the product (content) is immediately upon purchase (payment of the product invoice) on the private portal. So, the client already has access; there is no need to gift a product once it is purchased by the client. The client just needs to log into her private client website and go to the 'My Products' tab to access her product(s).
If the product contains courses, they can be accessed either by clicking on the name of the product on the client's 'My Products' page to go the the product's content list, or by going to the 'My Courses' page via the private client menu.
Important: The buyer of the product will be sent the login instructions immediately upon purchase via email with the message 'How to access $PRODUCT_NAME$' that the system adds automatically to every new product you create in Billing menu > Products > edit product > tab 'Autoresponder messages'. If, for whatever reason, you happen to delete this message from the product autoresponder series and you do not provide the login information to the buyer anywhere else, then the buyer will not know how to login and access their product content. So, you need to keep this aspect in mind if you want the buyer of a product to be able to access their product.