Is Google's recaptcha connected correctly on the ajax site?

Question

reCAPTCHA

Good afternoon, dear readers of the toaster. I've been fiddling with google recaptcha here, trying to bind it to a form that is sent to the server using ajax. Noticed the following:
if you get the recaptcha value

recaptcha=document.getElementById("g-recaptcha-response").value;

Then we essentially get an answer whether the person passed the validation or not.
This data can be sent for processing using php, or you can ask a person to pass validation using recaptcha.
Those. when clicking on the "send" button, we have null if the check fails and a certain string of characters if yes.

The question is how correct this method is. There are no similar things somehow in the documentation, and on the Internet too. Although, maybe I didn't search well.