I am sure you are informing me of terms of service that have been legally sealed, but I am wondering how that works in the case of an entrepreneur or investor who owns the product but has no clue about how to download files and make them them available to someone else? Or a busy executive who wants to hire someone to run their stuff. Not allowed? Why? Because the license says so, but what is the reason for enforcing that?
I noticed that when I installed Xenforo, it did not ask me to enter me license number. So in the above example, the OP can upgrade the forum of his client with his forum files. What I want to say is that as far as I have seen, there is no license check. Is that correct?
The files for each license can be different. This is certainly even more crucial if licenses have different expiry dates, or branding removal.
For example, if one of your licenses is active and the other expired on the 1st November, then you would only be allowed to install XF 1.5.2, and you wouldn't be permitted to install XF 1.5.3 or 1.5.4 (but for 1.5.4 you are allowed to use the released patch file). If a license has branding removal, the files for that license shouldn't be used on other sites otherwise you would be removing branding from a license where that isn't permitted.
I must stress, those aren't the only two cases apply, they are just significant. You should still use the right files for the right license, regardless.
You should be able to just upload the files, but make sure you replace the files with the same or newer version than you already have installed. e.g. if Site B is running version 1.5.4, you wouldn't be able to upload the files from 1.5.3. If you upload files which are newer than you had installed already, that's ok, but you would need to do an upgrade.
If you do happen to upload all of the files, and those files are from, say, version 1.5.3, then make sure you re-apply the 1.5.4 patch.