USB Host: Send HID Report of attached mouse

I am using an Arduino Leonardo and USB Host Shield. I have an USB Mouse plugged into the USB Host Shield and using the built-in HID Mouse of the Leonard to translate the buttons and movement of the slaved Mouse.

Is it possible to get the HID Report Description of the slaved mouse and pass that along to the computer instead of using the generic HID Report Descriptor? I'd like to make it so the computer thinks the Slaved Mouse is actually connected to the computer.