First problem would be powering the back, since the H backs do not have batteries built in. On my Hasselblad H3D-39 I use an image bank, but as far as I know the H4D series does not support the image bank. There are some 3rd party solutions that just supply power but I cannot remember them off hand. Your other option is tethering. Next problem... this may be limited to the H3D series, sync issues could be a problem. When I shot with it I saw horrible purple caste to image and extreme color shifts, getting worse at the higher shutter speeds. Originally I wrote this off to the fuji gx being a quirky camera to sync to, as syncing to a leaf back does not work with hardly any combination. Ok I said, how about something like the RZ67? I had no problems syncing it to my old leaf back in the past, this should be a piece of cake. RZ67 does the same thing, so this got me to investigate a bit. Turns out the H3D backs do not like early light, it seems to take a dark frame or do some sort of calibration BEFORE the shot, and when it gets hit by light early it screws it all up. The key then is to have the back start exposing before the shutter on the camera even opens. One inconvenient way of doing this setting the back's exposure time to something like 2 seconds, and manually triggering the back with a cable release, and then firing the shutter on the Fuji GX680 inside the exposure interval. Obviously this is not an easy way to shoot, so I came up with another more convenient to do the same thing.
I have not tried this with the fuji gx YET, but it fixed the problem completely on my rz67, and in principal should be the same. First, find a cheap electronic cable release on ebay with a 2.5mm jack you can put into the H3D, this is how you will be triggering your fuji gx now. For my rz, I spliced and soldered a cheap cable release into the electronic cable of the L-grip, so now the button on the l-grip can trigger my h3d. Ok, the h3d can be triggered now... whats next? The H3D backs have a flash OUTPUT port as well, take any generic 3.5mm male flash cable, and splice it into the electronic release for your fuji. Essentially, you are turning your H3D into a release for your Fuji. Now that is all done, simply press the button on your generic ebay cable release to trigger the h3d, the h3d will output a signal through the flash output into the fuji gx electronic cable, thus triggering the shutter. This should all happen seamlessly, and instantaneously. At least that is how it worked on my rz67, but I see no reason why the fuji would be any different. The important thing is the sensor begins exposing before the shutter on what ever system you are using opens and everything should be ok.
