What kind of cert is this (for server, email, CA)? Where are you trying to install it (People, Servers, Authorities tab)? What error message do you get?

Cert of mail. Error when trying to import the certificate (*.PFX) into Thunderbird. Error message is: "The operation PKCS #12 failed for unknown reasons".

Thunderbird does have CA certs in it's certificate store which do use SHA-256 as signature algorithm. So it isn't a Thunderbird restriction per se. What's wrong with the cert you're trying to import, I don't know. Do you see anything in the error console?

The certificate is fine. Installed in the web browser, the system (Windows 8.1 Pro). Just not in Thunderbird. The only difference in the certificate is the one that is " sha1RSA", not "sha256RSA". I do not see any bugs except the message that I wrote. I do not know what error console you wrote.

Tools (Alt-T) - Error Console

If you where able to import the cert into the Windows certificate store you may try to export it from there, and then try to import it into Thunderbird again. If this is your own cert, make sure you also include the private key when exporting. You may be prompted for a passphrase to protect the private key when exporting the cert.

Export the certificate from the system, the only way to use it later (installed automatically). After export, easily imported back into the system ... but not in THUNDERBIRD. I think that this limitation or error in THUNDERBIRD. The console does not display any error.