On both domains, place an image or other web element that is pulled from the other domain. Use the URL to notify the other domain that user X is on domain A, and let domain B associate that user ID with that user on their system.
It’s a little complex to carry out correctly, but if you think it through it’ll work out very well.
Vinko points out in a comment (thanks!) that I shouldn’t take it for granted that you understand the security risks involved. If this information is of any value to anyone, then you should make sure you use proper encryption, authentication, etc to avoid releasing sensitive information and to avoid various attacks (replay, man in the middle, etc). This shouldn’t be too onerous since you control both websites and you can select a secure secret key for both, since the communication is only going between the two servers via this special URL. Keep it in mind though.
-Adam