Hello Gregor,
The file block is just another block in the composer in which you can upload the PDF and insert it with a download link. The file that is responsible to be generated with the PDF output is located at /components/com_easyblog/themes/wireframe/blogs/blocks/pdf.php
I am not sure if this could work but you can try replacing the contents of that file with the following codes,
<div class="eb-pdf-viewer">
<object data="<?php echo $block->data->url;?>" type="application/pdf" width="100%" height="<?php echo $block->data->height;?>" class="pdf-viewer-browser">
<iframe src="<?php echo $block->data->url;?>" width="100%" height="<?php echo $block->data->height;?>" scrolling="no" frameborder="0" allowTransparency="true">
<?php echo JText::_('COM_EASYBLOG_BROWSER_DOES_NOT_SUPPORT_PDF_VIEWER'); ?><br />
<a href="<?php echo $block->data->url;?>"><?php echo JText::_('COM_EASYBLOG_DOWNLOAD_PDF_FILE');?></a>
</iframe>
</object>
<div class="pdf-viewer-button">
<a href="<?php echo $block->data->url;?>" target="_blank" class="btn btn-default"><i class="fa fa-download"></i> <?php echo JText::_('COM_EASYBLOG_DOWNLOAD_PDF_FILE');?></a>
</div>
</div>
Then re-save your post again.