What you are asking makes no sense. Thunderbird only receives messages from your provider when open and running. You indicate after you get notification of a new mail you would open Thunderbird. Go to the providers web mail site for your secondary account and see what they offer. I imagine it will be just to forward the message to your primary account.

re :I have 2 email accounts -one on TB & one with another email provider which is my default email address.

Email addresses are provided by ISP, webhosting package or freely obtained from eg: gmail. Thunderbird is not an email provider; nor a server and does not provide email addresses. It is an email client. A program running on your computer with the ability to show all emails from all email addresses, which may be received on different servers.

Emails are held on the server until you open Thunderbird and then it will retrieve from server. So, Thunderbird has no knowledge of the email received on the server until it accesses the server, so it cannot forward to the other 'B' email address nor send a template message saying 'look for email in TB'. This would also be fultile as you have already started TB, so can see the email anyway.

Senario: If Thunderbird was started and running on a different computer eg: Laptop and you were using a different computer eg; desktop Then any or specific auto downloaded emails into Thunderbird on Laptop could be instructed to trigger an email to the 'B' main mail account. So if you are only viewing 'B' mail account on desktop, at least you would know about checking Thunderbird on the laptop.

What you ideally need is for the webmail account of email address 'A' to be able to set up a simple message template to send to your other main 'B' email address, which you understand to mean, email has been received in 'A'. Then start TB, download email. However, this may not be possible. I cannot do this from any of Usually, they either allow complete forwarding of emails from server to another server/email address or they allow an 'Out of Office' type of auto response which would be sent to the person who sent the email. Neither being what you need.

If Thunderbird is already started and operating as a window in the background of desktop or minimised to Task Bar, you can set up email alerts, which pop up in the bottom right corner of screen drawing your attention to new mail in the Inbox. 'Tools' > 'Options' > General tab Alerts can be visual pop up, or simply show an envelope tray icon or play a sound or any combination.

You could add your mainly used email address to Thunderbird and set it up to be the default account and view all emails in the one place.

Mail accounts can be 'collapsed', so only displaying the mail account name until you need to access those folders. POP mail accounts can also be setup as deferred accounts or more commly known as Global Accounts. then emails are received into 'Local Folders' and there is no visible mentioning of the email address in the Folder Pane.

Thank you both - I have a clearer understanding of what can be done. I am trying to do something for an organisation that uses volunteers who use personal email addresses. We handle extremely confidential information and wish the volunteers to have an 'organisation' email address which can be provided by a web server. However, having to open two email accounts on a regular basis just in case, the 'organisational' account has received an email does lead to the possibility of an email being 'unread' which is not acceptable. While the email could be forwarded to the personal email address, this is not necessarily confidential as other users can use that address - a notification that an email has been received by the organisational account on the personal email address that would then require the logging on to the 'organisational' account would be ideal. I will have to look further into this as to whether it could be possible for the 'organisation' account to do this. Many thanks for your time in answering my question