Map Users from one AD Domain to Another

[Guest]

Is there any relatively painless way for me to map users from one AD Domain to another AD Domain? For example: I want to copy Group Members from AD1 to AD2. The User ID do not match. How can I map AD1\Smith to AD2\john.smith so that I can say all of the members of AD1\GroupA should be added to AD2\GroupB and have AD1\Smith in AD1\GroupA be automatically converted to AD2\john.smith in AD2\GroupB?

Thanks for any advice you all might provide.

Dan G