To do so, just open the 'Extensions' tray in Facebook Messenger, select PayPal, and create the invoice. The buyer hits the button marked 'Pay with PayPal' and completes the transaction using the platform's One Pay system.
Sure, it's just a plugin that routes existing PayPal functionality through Facebook Messenger's chat. But it's a lot more convenient to bring services into an existing conversation than send a buyer off to an external site. It's certainly useful for more professional exchanges, especially to preserve purchases within a chronology of interactions, a la Slack. But there's nothing stopping you from using PayPal to invoice for self-employed or private business.