Get mail for all accounts
From MozillaZine Knowledge Base
If you have more than one e-mail account and you want to get mail from all accounts at once, click on the drop down arrow next to the "Get Mail" button and select "Get All New Messages". Alternatively, you can also use the keyboard shortcut "Ctrl+Shift+T".
If for some reason you don't get the drop down arrow try installing the Easy Get Mail Button extension. You can find several obsolete extensions with similar names (for example Get All Mail Button) on web sites. This is the only one that seems to be actively maintained.