In TheBat program at the certifications database you should:
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remove certifications regarding to the used email server (e.g. for GMAIL they will be tagged as "pop.gmail.com" and "smtp.gmail.com"),
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disable the email program and enable it again,
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then the question about the certification should appear: you should add it to “trusted”. You get to TheBat certifications database via address book (menu “Look->Certifications database”)
In the Thunderbird program you should select:
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menu "Tools -> Options -> Advanced”, select „Certifications” fold, press “Display certifications” and select “Servers” fold. Remove used email servers (but only certifications for these servers, not the servers themselves), and press “OK” and the “OK” in previous window,
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now, to be sure, disable and enable Thunderbird again,
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when during the attempt to receive/send email the program asks for the certification, you should select “Confirm security exeption” at the „Keep this exception permanently” ticked.