partitioning - Migrating one partition to SSD in a way that allows booting?

I've got a Windows Installation, with a partition table that looks like this:

 Volume ###  Ltr  Label        Fs     Type        Size     Status     Info
  ----------  ---  -----------  -----  ----------  -------  ---------  --------
  Volume 0     D                       DVD-ROM         0 B  No Media
  Volume 1     E                       DVD-ROM         0 B  No Media
  Volume 2         Recovery     NTFS   Partition    300 MB  Healthy
  Volume 3     C                NTFS   Partition     51 GB  Healthy    Boot
  Volume 4     H                NTFS   Partition   2742 GB  Healthy    Pagefile
  Volume 5                      NTFS   Partition    450 MB  Healthy
  Volume 6                      FAT32  Partition     99 MB  Healthy    System

I'd like to migrate Windows to a SSD, but the trick is that H: contains all of my files, so I only need to migrate the 50GB C:.

I've tried copying C: to the partition using GParted on an Ubuntu Live CD, and while the files copy just fine, I can't boot from the drive.

I can't clone the whole drive, since it's 3TB and the SSD is only 240GB. So, how can I clone just the Windows partition in a way that preserves the Windows Boot Manager, MBR, etc.