The fake account sounds like it is an alias account for your primary account. That allows you to use it, but it is dependent on the primary account. My suggestion is to set it up in Thunderbird by clicking 'account settings', then highlight your primary account in left side, and then click the 'manage identities' button on right side of screen. There, set up your alias. This lets you compose messages, using the dropdown menu on FROM line and incoming messages will appear within the primary account.

@david Thanks for your response.

The term "fake" is misleading. A better name would have been "alternative". Sorry about that.

The alternative account is used to protect my ID on sites such as forums, or for people who ask for my email in pubs.

Both emails can be accessed at gmail.com in a browser

Thanks

Please post screenshot of the error message received when attempting to send message. Since you can receive, but not send, my initial guess is that you may be using the SMTP server for the other account. Easy to do. Try this: - click 'account settings' pane - click the name of the alternate account in left side of screen - look at lower right where it shows 'outgoing server' and click 'edit outgoing server' - is the email address shown there the alternate email address?