Session variables live within the websites own memory process.
For security websites can not read the memory of another website, so the session variables cannot be passed between the two websites.
The only way the existing membership API will work is if you move the forum to the same website and have it in a subfolder rather than a subdomain.
There is also the 'Web Wiz Forums XML HTTP API' which can be used to login to the forum from another website. The XML HTTP API is allot more powerful, but would require programming skills in order to be able to use it. The page below has more details;