In order to have a cross-domain access to my test instance of SQL Server I need a login with a database user and not with a Windows user.
Once this would work I could start doing this from my *NIX environment, but basically Windows won't let me access the DB this way and throws an authentication error 28000/SQL Server Error 18456.
I already did
ALTER LOGIN [administrator] WITH DEFAULT_DATABASE=[...]
ALTER LOGIN [administrator] WITH PASSWORD=...