Since Serhii currently has a few days off, I will replace him here in the forum.
I hope this is OK for you.
I am seriously sorry about the delay, I can not change it, but I can fix it for you.
The issue now is I can not login to the site.
The Site is Currently in Offline Mode.
ERRORE: La password inserita per il nome utente agenzia non è corretta. Password dimenticata?
Therefore I can not check it online.
1. The issue is not known, and not reproducible locally.
2. It is there fore a issue on your server or with a Plugin / Theme you use.
3. Since this happens since the new host, it might be a permission issue such as mod_security making it impossible for AJAX requests to be handled.
Can I ask you for a Site's Snapshot?
We usually recommend the free Plugin "Duplicator" for this porpoise.
If you already know how Duplicator works
(http://wordpress.org/plugins/duplicator/),
please skip the following steps and just send me the installer file and the zipped package you downloaded.
★ Duplicator Instructions
hidden link
Send me both files (you probably want to use DropBox, Google Drive, or similar services, as the snapshot file will be quite big)
❌ IMPORTANT ❌
Remember to create or keep an admin account for me before creating the snapshot, or I won't be able to login. You may delete the new admin account once the snapshot has been built.
I will enable your next answer as private so you can provide me the information securely.