HC-05 to HID Connection?

I have been working on a remote controlled motor for a while now and I have been looking for a device that would work as a suitable remote. I need a joystick and a few buttons. I stumbled upon this: controller, a few weeks ago at Walmart on the clearance rack for $3, so I picked a few up. I opened one up and found it has an ST17H25 module inside, which unfortunately was a dead end as there is little to no documentation online. Next, I decided to just intercept the signals using an HC-05 bt module, but I am having trouble getting it going.

My question is: How should I go about connecting this Bluetooth controller to the HC-05 and once I have it connected, how do I watch all incoming transmissions and reassign those signals to act how I want them to?

Thank you for any help you can provide.

Since this device is for use with a phone, it will probably be a slave. This means that HC-05 must be confugured as a master. I assume you have done that.
One problem may be the protocol used. The HC-05 is a plain-vanilla SPP device, and I don't think that can be changed.
Another problem might be hinted at by the fact that you got this thing for $3.

Well, I have tested it and it does connect to my phone. I think the fact that is $3 makes me think it will also be quite vanilla. Can you expand on what you mean by the protocol may be an issue? Thank you for the reply

I'm afraid I can't recall much about it. The SPP protocol is just a wireless serial for data, but there are others that I think are used for video and sound, and I don't think HC-05 is up for that. I don't think Arduino is either.

Your "Connect to phone" does not mean HC-05 can connect to it, and even if HC-05 can see it, it doesn't mean it can connect to it and do something useful. It may simply mean that the accompanying software configures Android's bluetooth to depart from the standard SPP mode in order to talk to the device.

Google has plenty of stuff on protocols, SPP is a keyword. You may be able to get some joy by using a different bluetooth on Arduino.

The $3 made me more inclined to think the device is a dud.