How to implement a captcha solution on a third-party resource?

Question

PHP

Friends, welcome. Immediately describe the situation, and then the resulting questions.
Situation:
I have a site where users are authorized on a third-party resource, and then the personal account page and other values ​​are parsed. (Implemented on curl) But at the moment, authorization on these services takes place with captcha (recapcha v2 inclusive). So: of course, I don’t pretend to automatically enter captchas and write AI, but I thought to solve the problem in a slightly different way. Same as antigate. That is, I need the captcha to be sent from the resource to my site, where the user solves it, and then authorization takes place using curl.
Questions:
1) Is it possible to implement this?
2) In which direction to google?
3) What documentation to thoroughly study?
I need a tip, or maybe this problem has already been solved somewhere (although I did not find it).
It’s just that if antigate has a solution at all through the left resource through the left users (+ I was somewhat surprised that even a captcha with a choice of pictures is solved there), then I think that the problem is solvable and not in the most difficult way.
Many thanks in advance for the detailed answer.