In the new domain, create a folder for the new profile.
Use Control Panel / System / User Profiles and select the profile. Press Copy To. Type or Browse to the folder in the new domain. Click the Change button and select the new domain name. Select the user account of the user who is permitted to use this profile in the Names box. Click OK until all open dialog boxes are closed.
NOTE: The permissions are stored in the NTUSER.xxx file.