Finally I found the problem and a solution. The problem was, that my webhosting provider loads different php extensions in browser than in console. The driver pdo_sqlite was missing in console-php. Because I can’t enable php extensions by myself I used the app OCC Web to convert the database type.
Because the prompt “Continue with this conversion?” fails in OCC Web I simply disabled this prompt in the ConvertType.php as described here: Converting DB Type with single command
My database was that big that php ran out of time while converting, so I disabled in the ConvertType.php the conversion of some tables and convert them manually.
This issue can be closed than 