1. First, shut down VirtualBox.
2. With the iPhone connected, go to the settings for your Winduhs machine in VirtualBox and create a new USB filter from the iPhone (in recovery mode). Delete all the information except for the Vendor ID and save the new settings. Now, close the VirtualBox itself.
3. The trick is to run VirtualBox as root. This takes care of any permission problems. In order to do so, you need to have the same .VirtualBox file available to root. Simply make a symbolic link:
$ sudo ln -s /home/yourUsername/.VirtualBox/ ~root
Note: make sure to remove any previous .VirtualBox directory there may have been.
4. Now, you are ready to run VirtualBox as root:
$ sudo VirtualBox
5. Your iPhone should automatically be detected by iTunes. You will first have to restore it to factory settings. Once that is done, you may restore it to a backed up version.