A.K.A. WordPress and moodle SSO (Single Sign On).
There are these two very good open source content management and e-learning products:
I find this a very interesting argument, for this reason i started writing a guide about how to make users authenticate on both systems with a single sign on.
My post is about getting things running smoothly after wordpress updates.
That could be tricky because any updat on wordpress side or on moodle side will overwrite all modification made in order to make the SSO working.
You can take a look at my post about Moodle and WordPress integration.
Let me know if this works for you and what can goes wrong so I can update information there.