What I want to my site is to transfer the folder "mysite.com/modules/ipboard" to "mysite.com/forum/"

Is that possible?

One cheating way would be to set up a subdomain in your webhost panel - and get forum.websitename.com to point to http://www.websitename.com/modules/forum ....

Yeah... I have that, but when I go to http://forum.animekensei.com it appears in the adress bar http://www.animekensei.com/modules/ipboard/

Based on what I know about the way XOOPS works and the way modules work and the coding of them (using XOOP_URL and the likes), I seriously doubt you can do this. However, if you just want to promote a shortcut there, you can do that and redirect to the longer URL. Is there a reason that you want it to have a shorter URL?

Alternatively, ipboard is available as a standalone and you could run it outside of XOOPS in a forums directory. But, if you're using XOOPS for other stuff, you'll have to be okay with the directory structure that XOOPS brings to the board.

If you're replace an old forum at /forums with a new one using XOOPS, then trap the old URL and forward it to the new one.

what you can do is use a blank module, create an iframe that loads the exterior content, then place a xoops_version file into that directory (so that XOOPS recognizes it as an integral part of the current instaltion).
That's what works for me.