Will this work with a Manfrotto 393-H?
By itself, I would say no (based upon the photos I am seeing). You would need the Manfrotto 384 Dove Tail Quick Release System SKU: BG384. That comes with the base that screws onto any tripod where the camera would screw onto the tripod and the piece that screws onto the camera itself.
The piece that you show seems to be just the piece that connects to the camera. This would be fine if you already have the base plate.
Separately, I should point out that the tripod that comes up when I entered Manfrotto 393-H only holds five pounds. Make sure your camera and lens meets this requirement. If you are close to this limit, look for a heftier tripod.
I should also point out that I have done a no-no and left my camera in when carrying the tripod. My camera has fallen out twice and hit the ground. Disconnect the camera or at the very minimum keep the camera strap around your neck.