[Samba] accessing foreign AD users to NT domain

[Piviul]

Hi all, I'm planning to migrate a NT domain to a AD domain. Someone 
suggested me to create a new AD domain, then add manually users to AD 
with the same username and password of the NT domain and then join every 
PC to the new AD domain. This way the migration should be flawlessly 
because in a windows network a user can works on foreign resources 
(resources that are shared from server joined to other domains) if he 
shares same username and password. On my network that's doesn't seems to 
works.

I have a samba3 (4.1.17-Debian) NT domain, I have a new AD domain 
(4.10.4) and I have a user in AD domain with the same credentials in the 
NT domain. I have joined a  windows PC to the AD domain and when the 
user logon to the PC he can successfully works on all pc/server 
_windows_ shares joined to NT domain but can't on _samba_ shares joined 
to the NT domain.

Please can someone help me to troubleshoot the problem?

Thank you very much

Piviul