How to make Contact Form 7 and WP Post Popup plugins interact?

Question

WordPress

Good afternoon.

I use Contact Form 7 and WP Post Popup plugins to implement a popup feedback form. The popup markup is set on a separate page, and the Contact Form 7 form is inserted through the shortcode. In the body of other pages, there are elements with the modal-link class and the href attribute pointing to the page with the popup markup. When you click on these elements, the window with the form is displayed correctly, but when submitting the form, an error occurs - redirection to a page with the following content:

{"code":"rest_no_route","message":"Подходящий маршрут для и метода запроса не найден","data":{"status":404}}