Please make a backup before testing this because I'm not 100% sure it will work flawless.
I think the way to do it is something like this (untested):
Format one partition that will be your destination for the installation (I suggest you to choose the ext4 format)
Copy the your files and folders from wubi to the new partition
Make sure you have a folder named /boot/ with at least two files like initrd.img-2.6.38-10-generic and vmlinuz-2.6.38-10-generic
Than you will have to install grub:
These instructions were adapted from: https://wiki.ubuntu.com/Grub2#Recover
"METHOD 3 - CHROOT
This method of installation uses the chroot command to gain access to the broken system's files. Once the chroot command is issued, the LiveCD (in your case the wubi installation) treats the broken system's / as its own. Commands run in a chroot environment will affect the broken systems filesystems and not those of the LiveCD.
1) Boot to the LiveCD Desktop (Ubuntu 9.10 or later) (Open Ubuntu at Wubi). Please note that the Live CD must be the same as the system you are fixing - either 32-bit or 64-bit (if not then the chroot will fail).
2) Open a terminal - Applications, Accessories, Terminal.
3) Determine your normal system partition - (the switch is a lowercase "L")
sudo fdisk -l
If you aren't sure, run
Look for the correct disk size and ext3 or ext4 format.
4) Mount your normal system partition:
Substitute the correct partition: sda1, sdb5, etc.
sudo mount /dev/sdXX /mnt
# Example: sudo mount /dev/sda1 /mnt
5) Only if you have a separate boot partition:
sdYY is the /boot partition designation (for example sdb3)
sudo mount /dev/sdYY /mnt/boot
Mount the critical virtual filesystems:
sudo mount --bind /dev /mnt/dev
sudo mount --bind /dev/pts /mnt/dev/pts
sudo mount --bind /proc /mnt/proc
sudo mount --bind /sys /mnt/sys
Chroot into your normal system device:
sudo chroot /mnt
8) If there is no /boot/grub/grub.cfg or it's not correct, create one using
Reinstall GRUB 2:
Substitute the correct device - sda, sdb, etc. Do not specify a partition number.
10) Verify the install (use the correct device, for example sda. Do not specify a partition):
sudo grub-install --recheck /dev/sdX
Exit chroot: CTRL-D on keyboard
Unmount virtual filesystems:
sudo umount /mnt/dev/pts
sudo umount /mnt/dev
sudo umount /mnt/proc
sudo umount /mnt/sys
If you mounted a separate /boot partition:
sudo umount /mnt/boot
Unmount the LiveCD's /usr directory:
sudo umount /mnt/usr
Unmount last device:
sudo umount /mnt