LWSSO between different domains (SMA-SM Portal to SM)

We have SMA-Service Manager installed on windows servers and SMA-SM installed on Linux.

I have now reached the part of the configuration where I have to set up LWSSO between SMA-SM and Service Manager:

"Now you can configure LS-SSO in the Service Manager server. The Service Manager server must use the same domain and encryption key (initString) as SMA."

The problem is that our company have the Linux servers in one domain and the windows servers in another domain.

Has anyone had this problem? Any advice is much appreciated.