Move WUBI installation of Ubuntu to a different partition in Windows

I don't have a lot of space on my D: drive and Ubuntu is taking 15 gigs of it so I wonder, is there a way of moving Ubuntu from D: to C: while keeping the files that exists on Ubuntu?
Thanks

1. Make backup copy of all important data in Ubuntu into an external device. If the following does not work, you may lose all your data.
2. Copy the root.disk file from D:\Ubuntu\Disks to a safe place. You may put it in your "My Documents" for the time being.
3. Uninstall Ubuntu using Control Panel.
4. Reboot.
5. Install Ubuntu in C: using WUBI. Make sure when installing to C: that you choose the same Disk Size as the Disk you already have. This prevents errors.
6. Replace C:\Ubuntu\Disks\root.disk with the root.disk you had copied before.
7. Reboot.

One more step

See https://askubuntu.com/a/55029/14916 for details (Thanks to @bcbc for pointing out this part.) The following is taken from that answer:

e.g. if D: is /dev/sda2 and C: is /dev/sda1, then you'd hit 'e' on the first entry of the grub menu and change:

set root=(hd0,2) becomes set root=(hd0,1)

Delete the line - search --no-floppy xxx (as this overrides the previous set root command using the old UUID)

linux /boot/vmlinuz-xxxx root=/dev/sda2 ... becomes linux /boot/vmlinuz-xxx root=/dev/sda1 ...

This is a one-time override - hit Ctrl+X to boot, and make sure you run sudo update-grub after booting to fix the grub.cfg menu so it works the next time.

PS: There may be some variations. (hd0,2) could be (hd0, msdos2) or (/dev/sda, msdos2) depending on the version of Grub. Also root=/dev/sda2 may be root=UUID=xxxxx