My client has a Shopify site that processes card payments for all customer orders.
He has asked if it is possible to set something up in Shopify so that one of his customers can order goods but not make payment via the site, and then he can bill them the total amount on account every month. Is there as way of doing this?
You can create custom payment methods in Settings -> Payments.
In the 'Manual payment methods' section, click the drop down, and the first option will be 'Create Custom Payment Method'
A payment method called 'Monthly Billing' or something similar can be created. However, this will be visible to all customers at checkout. So it will be a good idea to include details to the effect of 'For approved customers only. If this payment method is used and you are not approved, your order will not be fulfilled and will be cancelled.'
The verbiage I inserted here is just an example, of course, and your client should choose the best verbiage that fits his/her business and customer.
It would be up to you to set up the invoicing system in whatever manner you see fit.
You can disable all other payment options in your settings and make this manual payment option the only one available. Then all customers will have to choose it as their payment method.