so I checked source code by myself and find solution for my problem with
Nginx + rest.php (see previous emails).
I don't know why, but Nginx need one more header in 401 response. So I
edited "include/fatal.php" file and added one line (bold):
*header('WWW-Authenticate: Basic realm="My Realm"');*
header("HTTP/1.0 401 Unauthorized");
Without this header, Nginx is not asking for credentials on "rest.php"
file, so it was not possible to use dl with Thunderbird.
I can't check it on Apache though, so I don't know if this solution
broke something else or not. If someone can check it on Apache, than
maybe author can integrate this header in next version of DL.