I've edited the paths and bingo, 100% and a new Washing machine.
The temporary folder has been created.

Edited:

$htmldir = '/var/www/vhosts/yabbtest.de/httpdocs/yabbfiles';          # Base Path for all public-html files and folders
 $facesdir = '/var/www/vhosts/yabbtest.de/httpdocs/yabbfiles/avatars';
                                                                       # Base Path for all avatar files
 $uploaddir = '/var/www/vhosts/yabbtest.de/httpdocs/yabbfiles/Attachments';
                                                                       # Base Path for all attachment files
 $pmuploaddir = '/var/www/vhosts/yabbtest.de/httpdocs/yabbfiles/PMAttachments';
                                                                       # Base Path for pm attachment files
 $modimgdir = '/var/www/vhosts/yabbtest.de/httpdocs/yabbfiles/ModImages';
                                                                       # Base Path for all mod images 

The paths are set in the setup and not in the Convert.

Edited:

I have now come by chance.
But next: The setuproutine runs perfectly in German.
But: From Convert2 it is despite translation only in English. I have looked at the Setup.pl and the Convert2.pl. The devil is in the details.
Since I think, I simply times the German Convert.lng over the English copied. Is working. So you should also look at the Setup.pl and the Convert2.pl, possibly also the ConvertLang.pl.

Build 1909

Paths must still be adapted manually before the conversion.

Build 1910

That's how it looks

$lastsaved = 'Administrator';
 $lastdate = '1506916022';                                             ########## Directories ##########

 $boardurl = 'http://yabbtest.de/cgi-bin/yabb2';                       # URL of your board's folder (without trailing '/')
 $boarddir = '/var/www/vhosts/yabbtest.de/cgi-bin/yabb2';              # The server path to the board's folder (usually can be left as '.')
 $boardsdir = '/var/www/vhosts/yabbtest.de/cgi-bin/yabb2/Boards';      # Directory with board data files
 $datadir = '/var/www/vhosts/yabbtest.de/cgi-bin/yabb2/Messages';      # Directory with messages
 $memberdir = '/var/www/vhosts/yabbtest.de/cgi-bin/yabb2/Members';
                                                                       # Directory with member files
 $sourcedir = '/var/www/vhosts/yabbtest.de/cgi-bin/yabb2/Sources';
                                                                       # Directory with YaBB source files
 $admindir = '/var/www/vhosts/yabbtest.de/cgi-bin/yabb2/Admin';        # Directory with YaBB admin source files
 $vardir = '/var/www/vhosts/yabbtest.de/cgi-bin/yabb2/Variables';      # Directory with variable files
 $langdir = '/var/www/vhosts/yabbtest.de/cgi-bin/yabb2/Languages';
                                                                       # Directory with Language files and folders
 $helpfile = '/var/www/vhosts/yabbtest.de/cgi-bin/yabb2/Help';         # Directory with Help files and folders
 $templatesdir = '/var/www/vhosts/yabbtest.de/cgi-bin/yabb2/Templates';# Directory with template files and folders
 $htmldir = '/var/www/vhosts/yabbtest.de/yabbfiles';                   # Base Path for all public-html files and folders
 $facesdir = '/var/www/vhosts/yabbtest.de/yabbfiles/avatars';          # Base Path for all avatar files
 $uploaddir = '/var/www/vhosts/yabbtest.de/yabbfiles/Attachments';
                                                                       # Base Path for all attachment files
 $pmuploaddir = '/var/www/vhosts/yabbtest.de/yabbfiles/PMAttachments';
                                                                       # Base Path for all PM attachment files
 $modimgdir = '/var/www/vhosts/yabbtest.de/yabbfiles/ModImages';       # Base Path for all mod images

 ########## URLs ##########

 $yyhtml_root = 'http://yabbtest.de/yabbfiles';                        # Base URL for all html/css files and folders
 $facesurl = 'http://yabbtest.de/yabbfiles/avatars';                   # Base URL for all avatar files
 $uploadurl = 'http://yabbtest.de/yabbfiles/Attachments';              # Base URL for all attachment files
 $pmuploadurl = 'http://yabbtest.de/yabbfiles/PMAttachments';          # Base URL for all PM attachment files
 $modimgurl = 'http://yabbtest.de/yabbfiles/ModImages';                # Base URL for all mod images

 1;
  

All the html directory paths are based off $htmldir and and all the html urls are based off $yyhtml_url.  This means if $htmldir is wrong then all the paths to the html folder will be wrong.

$htmldir and $yyhtml_url are inputted separately and there's no cross sharing of data. I'm still suspecting that you're not adding the 'httpdocs/' into the $htmldir textbox where it belongs. In fact, since you know what that path is supposed to be, there's no reason you can't just copy the entire path into that box.

This is from my testbed - for you, the highlighted section needs edited to be

/var/www/vhosts/yabbtest.de/httpdocs/yabbfiles 

while the textbox beneath needs to be

http://yabbtest.de/yabbfiles 

The script cannot actually detect where the directory is. The path and url in that section are 'guesses' since on most servers, yabbfiles will be on the same level as cgi-bin and both will be inside a 'httpdocs' or 'public_html' folder. So based on where YaBB.pl is, yabbfiles would normally be up two directory levels from YaBB.pl.

In the second attachment you can see that on my server, I have to edit both the htmldir path and the html url path.