Move Posts from one DB to another

I have a project where we installed a new instance of WordPress to replace an existing one but now we need to find a way to get the old site posts and content (mp3 files mainly) put into the new site.

Long story short… don’t ask why we did it this way but now we need to get the old databases posts and content into the new site.

Can anyone recommend the best way to do this? By the way, both sites are on the same server.