Is it possible to move a forum to an existing suite site that does not currently have one? 

Can you retain the users and their log ins from both sites?

 

 

You can export your users from one install and import into the other.

You can also use the converter to convert one Invision Community into the other.

Thanks!

That can't be something I can do on CIC though is it? 

 

Yes, you can do this on CiC as well. Visit the member list in your AdminCP, and the export and import options are buttons at the top right.

Converting can also be done, but you will need to submit a ticket to do so.