A device has been developed with moveable liquid nitrogen and liquid helium volumes that is capable of reaching over two meters into the coldest regions of a cryostat or dilution refrigerator and reliably extracting or installing a target of solid, polarized hydrogen deuteride (HD). This Transfer Cryostat incorporates a cylindrical neodymium rare-earth magnet that is configured as a Halbach dipole, which is maintained at 77 K and produces a 0.1 T field around the HD target. Multiple layers provide a hermetic 77 K-shield as the device is used to maintain a target at 2 K during a transfer between cryostats. Tests with frozen-spin HD show negligible polarization loss for either H or D over typical transfer periods. Multiple target transfers with this apparatus have shown an overall reliability of about 95% per transfer, which is a significant improvement over earlier versions of the device.