Grant a login of Sql server authentication the same permission of a Windows group login with Windows authentication?
At the database level, you could simply add both to the same database role. Of course, when you create the role, you'll have to grant it all the same permissions as the existing group, but you only have to do that once. 

At the server level, to do that without re-applying all of the permissions (which you could probably script without a whole lot of effort - you can get some ideas here), you'll have to wait for SQL Server 2012, unless you can use a fixed server role.