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Sounds like openID to me. Formulize doesn't really do this kind of thing. The Registration Codes module, a companion to Formulize, lets you have codes that users can use to register for your XOOPS site, and depending on the code, they can be automatically granted immediate access to the website and membership in certain groups.
Perhaps you could make those codes available in a secure way on another website, and then users could use the code to register for the XOOPS site. ie: you would trust that the code has been distributed only to the right people, so you immediately allow them into your XOOPS site, and the code would cause them to be automatically slotted into certain groups in your XOOPS site, which would indicate which part of the other site they had got the code from.
Maybe that would work?
Registration Codes is somewhat complex to setup, but the readme is quite detailed.
If you want to pursue this in more detail, feel free to post on our support forums at www.freeformsolutions.ca/formulize
--Julian