Showing Appointments+ calendar on non-WordPress site possible?

This might be a stupid question: I have a client who would like to show the calendar from Appointments+ on their existing non-WordPress site. I have already prepared a WordPress site for them with a single page just for booking appointments, which they are happy with.

Effectively, what I want is for a visitor to the non-WordPress site to use the Calendar to select and make a date for the appointment, but that all the data goes to my WordPress site so that it's all in the database and confirmations/reminders get sent out from WordPress.

Is anything like this possible? TIA.