What set up is required is for AX2012 CU3 to enable employees created in one company to approve invoices in other company. The employees are created in the company A, the invoice created in company B. If we open 'Approved by' list in company B, no employees in the list.
The solution you can find in the attached file.
The company in "System administration> Common> Users> Users" is the default company for the user. I.e. the company selected when the user starts the AX-client.
The AD-user, the employee and the relation between the two tables are all global - shared data for all companies.
Therefore your setup should be ok for all companies for the automatical setting of the employee. This automatic initialization of employee/worker takes place various places in AX. E.x. vendor invoice approval journal, purchase order, project.