Is this allowed?
 

My friend has got a vBulletin license, which he's not using and has offered to let me use it for free for a month or two, so I would like to install it onto my website, but hopefully in a month or two time I will have my own vBulletin license, so can I change the vBulletin license to my new one if I do purchase my own?

you could always redownload the install files, because your license id is embedded in the vb core files.

Maybe you can combine this procedure with an update

Technically no, you may not "lend" or rent out a vBulletin license.

Your friend could make his own forum and appoint you as an administrator and let you do whatever you want- and later when you get your own VB license he can "sell" you the site for $1 or whatever, but technically he needs to own the site his license is being used on.

You should probably ask on the pre-sales section of vbulletin.com for license issues.