The best thing to do is to set up all your e-mail accounts to use the same outgoing server and choose one that supports authenticated logon. If you can sign on to the outgoing DSL server, that will probably be your best choice. Go to the Outgoing Server tab and check the authentication box. Then input your logon credentials and test.
If you use the same SMTP server for all accounts and it supports authentication, you don't have to change anything when you change the connection type.