See https://support.mozilla.org/en-US/questions/1451180#answer-1659847

Enter the correct server names, then restart TB and change to OAuth2 for incoming and outgoing.

Thanks but what do you mean by the 'correct server names'? My imap server is: imap-mail.outlook.com - but that one does have the option for Oauth2, only it doesn't work. My outgoing server is: smtp-mail.outlook.com - this is the one where there is no Oauth2 option.

The correct server names are shown in the link in my first reply:

https://support.mozilla.org/en-US/questions/1417298#answer-1588949

That works and I can send and receive mail. Thank you all for your help. I do appreciate it. In your reply on the link you sent, you say State if you use a VPN or non-MS antivirus. Is this an issue as I use both?

A VPN can mask your true location, which affects authentication with some providers. Some VPNs have options to avoid email interruptions, but many do not.

The general recommendation is to add the TB profile folder as an exception or exclusion in AV settings, leaving the real-time background scan in effect, and to exclude AV scanning of secure (SSL) connections. There's a long history of AV apps blocking or otherwise interfering with TB.

Although I had no issues yesterday and was able to send and receive mail, I find that I can no longer send mail from TB today (receiving is OK). I have tried turning off my VPN but this doesn't help. I have attached some screenshots. (Note: the 1st screenshot gives me an option of 'Enter New Password' but it doesn't let me enter one.) Any idea what I'm doing wrong?

You shouldn't see that password prompt if the authentication is OAuth2. Check that your account is pointing to the correct smtp server, especially if you have multiple accounts and smtp servers:

https://support.mozilla.org/en-US/questions/1350593

I do have multiple accounts (one of the reasons for using TB) - a gmail and yahoo one. I checked the user name in the SMTP Server Settings and it is correct. I deleted the passwords for the hotmail account in Privacy & Settings. I then restarted TB. I still cannot send mail and got the same Retry/Enter new password/Cancel pop-up. It still won't let me enter a new password. (Strangely, I can receive mail even though I have deleted my passwords for the account!). Any ideas? (I do appreciate your help)

Sorry, forgot some images

I've no idea why you're seeing that password prompt if you've deleted all entries for the account from Saved Passwords and set the authentication to OAuth2. You can reset all password data by deleting logins.json, key4.db and cert9.db from the profile folder, with TB closed. They are automatically recreated on TB restart, but you will have to complete the OAuth2 authentication for all accounts, and maybe it will work for Hotmail.

Also, disable the VPN while doing this test. Check also you have no security/AV app managing passwords.