What are your incoming and outgoing server settings?

https://www.fastweb.it/fastmail/guida/mail_POPeIMAP/

Thank you for your reply. The outgoing setting is: server name: smtp.fastwebnet.it, port number 587. The weird thing concerns the incoming settings: the only working setting seems to be with port number 110, both with IMAP and POP access, even though it should be 110 with POP and 143 with IMAP. Now it works only with port number 110 and security protocol disabled. In any case, I still cannot retrieve my old emails; I didn't make the backup, but I thought I would have been able to retrieve them without the backup. Also, on my cell phone the incoming setting is set with IMAP access and port number 143, so is it normal to have two different working settings for two different devices? Thank you

POP and IMAP are different protocols. It's OK one to be on a port and the other one different... IMAP on a POP port should not work though... Can you add a screenshot with those settings used by that account?

You should use the settings with SSL/TLS security for the incoming and STARTTLS for the outgoing, but if your connection is refused, it may be because the server doesn't support the version of TLS required by TB 78:

https://support.mozilla.org/en-US/questions/1295861

sfhoves could be, if I use the settings with SSL/TLS security for incoming it doesn't work at all, it seems it takes too long to connect to the server and then it goes in timeout

@ffth202009 attached the print screens with different settings

It's not only about "sever address" it's also about the protocol. On all those pictures that account show as set with "pop" settings protocol. So then you should use 110 port... According with some websites you should also set: Authentication: Password SSL/TLS: No

Ffth202009 yes thanks for the hint, that's probably the reason why it works only with 110 port and no security settings and password for authentication. Can I only ask you why I still cannot see older emails? should I have done the backup even if the account settings have not changed? Thank you

Your first picture shows a POP account with POP settings, but the others show a POP account with IMAP settings. You can't change a POP account to IMAP just by changing the server settings - you have to add the account as a new IMAP account.

http://kb.mozillazine.org/Convert_a_POP_account_to_a_IMAP_account

Your problem may have nothing to do with the TLS version, but it's best to first test with the correct account type and settings.

Thank you, now I have created a new IMAP account but it works only with no security settings. I have also been able to restore my old deleted and sent emails. I wish I could retrieve my old Inbox as well.

If the IMAP account works but only with no security, you may want to try changing the preferences for TLS version. Perhaps try it in a separate profile, from Help/Troubleshooting, about:profiles. The current profile is not affected.

As for the old Inbox, it may still be in the profile, but in a subfolder that is older than the current account subfolder, i.e. in the Mail subfolder of the profile, look for subfolders named pop.fastwebnet.it, pop.fastwebnet-1.it, pop.fastwebnet-2.it etc. Check the dates on those folders, as one of the older ones may have the missing mail. Look for the mbox file named Inbox, with no extension, and copy it into Mail\Local Folders, with TB closed, renaming it to InboxOLD. Restart TB and there will be an InboxOLD folder under Local Folders in the Folder Pane.

Help/Troubleshooting, Profile Folder, Open Folder, to open the current profile.