I have Coppermine 1.4x installed inside phBB2 (as directed).
Who told you so? I have seen that people do that, but it's totaly silly and pointless. Won't help you in terms of bridging nor visual integration nor search engine friendliness. I wish I knew where people recommend that. Anyone who recommends that has got no idea at all.
Here's what I suggest you do in your situation:
1) Set coppermine offline. Go into coppermine's config and set if offline to make sure your visitors don't interact with coppermine while you perform your maintenance works
2) Unbridge temporarily: Go to coppermine's bridge manager and temporarily unbridge your gallery, making it a standalone app (for now)
3) Download the Coppermine folder (everything) to your local client using FTP
4) Upload the local copy of your coppermine folder to a folder on the server that resides outside of your forum's folder. Preferably (in terms of SEO) into a folder that means something, e.g. "gallery" within your webroot.
5) Go to your "new", moved coppermine install using
http://yoursite.tld/gallery/ or whatever name you picked. Go to coppermine's config
http://yoursite.tld/gallery/admin.php and change the coppermine URL there to reflect the move
6) Perform whatever steps are needed to upgrade your forum application. We have no idea how to do that, so you'll have to ask that somewhere else
7) Download the phpbb3 bridge from our site
8) Run the bridge manager (
http://yoursite.tld/gallery/bridgemgr.php) and bridge coppermine with your upgraded, phpbb3-driven forum
9) Go to coppermine's config and turn offline mode off, i.e. turn your gallery back online for the public
10) If everything works as expected, delete your "old" coppermine folder from
http://yoursite.tld//phBB2/coppermine/ using your FTP app