Preface:
I have found documentation showing how to do this, but not EXACTLY how I need to have this done.

My company recently purchase a new domain <new_domain.com> and would like to migrate all the users from <old_domain.com> to the new domain. However, they want the users to still get mail sent to <user@old_domain.com> and <user.alias@old_domain.com> but use <alias.user@new_domain.com> as the primary e-mail they send and recieve from. Is it possible to do this and have all the e-mail sent to @old_domain.com put in the inbox of @new_domain? or am I going to have to map the inbox of the old domain?