How can I edit posts.php?

We have documented this here:

https://docs.ultimatemember.com/category/118-templates

Hope that helps!

Yes I’ve read that but it doesn’t address my question

I’m talking specifically about posts.php

It addresses your question. The template that needs to be edited is templates/profile/posts.php

Please send us a ticket for further questions. We provide our support via our ticketing system.

Thanks

Do I keep that folder structure in my theme as well?

This is not a site specific question, it’s a clarification question on your website’s instructions.