Integrating Zoom into a website

I own an agency and we have a lot of clients who record podcast interviews on zoom. Currently, the clients have to download the recording afterwards, then upload it through the back end of our website. I would like to be able to embed or connect the client’s Zoom account to the back end of our website, so that when they are done recording an episode and they close the Zoom, the recording automatically gets uploaded to our website. Is that possible through Zoom?