How to set gravatar picture programmatically?

I'm using gravatar to display my user contact in WordPress but I want to allow them to change their picture. I don't see any way to set it with the API.

I'm not using Woocommerce and I already know to fetch the avatar. Is it possible?

Edit

After some search, I found in the api documentation, this section : https://fr.gravatar.com/site/implement/xmlrpc/

But I still don't understand how to implement it with my WordPress avatar.

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