Labor Transactions and Employee Business Group Assignments

Hi,

We have created one Business Group for the Country US and another Business Group for the Country UK.

We want to develop a customisation so that we create Labor transactions in projects.

We have an employee, employee A defined at employee level with a Organization 'ORGANIZATION A' associated to the Business Group for the Country US.

Can we enter a labor transaction for employee A in a responsibility associated to the UK Business Group ('ORGANIZATION B')? Or to do it we need to define the employee twice? One employee setup for 'ORGANIZATION A' (Busines Group US) and another setup for 'ORGANIZATION B' (Business Group UK)?