I had to change the file-links within the forum-messages from /components/com_fireboard/uploaded/files to /images/fbfiles/files. This was done by replacing the links in the database tables jos_fb_attachments and jos_fb_messages_text.
The SQL could be the following (if there is only one file per message), replacing siteurl, number, sitepath by what you need.
[code:1]UPDATE `jos_fb_messages_text`
SET message = concat(substr(message,1,LOCATE('siteurl/components/com_fireboard/uploaded',message)-1),
'siteurl/images/fbfiles', substr(message,LOCATE('siteurl/components/com_fireboard/uploaded',message)+ number))
WHERE message LIKE "%]siteurl/components/com_fireboard/uploaded%";

UPDATE `jos_fb_attachments`
SET filelocation = concat(substr(filelocation,1,LOCATE('sitepath/components/com_fireboard/uploaded',filelocation)-1),
'sitepath/images/fbfiles', substr(filelocation,LOCATE('sitepath/components/com_fireboard/uploaded',filelocation)+ number))
WHERE filelocation LIKE "%siteurl/components/com_fireboard/uploaded%";[/code:1]

I haven't had a chance to actually run these but they look like they solve all those broken image link issues when upgrading.