Achieving Single-Sign-On

You need to enable cookie based forms authentication for your site, as the forum uses forms authentication cookie to recognize logged in users. Single Sign On depends on the presence of forms authentication cookie.
 
In addition, you need to make sure that in both web.config files:

1. forms authentication cookie's name, protection, path are the identical.
2. you have identical machine key (validationKey, validation, decryptionKey)
   1. Get your machine key if you don't have one yet.

That's it. It shouldn't take more than 5 min to do the above.

Alternatively, you can read this article on creating a custom Forms Authentication Cookie for forum if your site configuration does not allow the above.