Two domains and same user name, can we merge

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http://serverfault.com – We have 2 domains(A,B) in our environment. When ever someone joins company his account will be created in domain A. If someone has to work in a particular department his account will be created in domain B. Both accounts will have same user name. Domain B have trust relationship with Domain A The department with domain B have many application/softwares/server(300+ windows and linux machines) and around 150 active users. Now the situation is- company wants us to make users use their Domain A account in all the domain B servers. Is there a way to achieve this? (HowTos)