What to do after getting hit at a truck stop?

Pretty simple question since this is my first time dealing with this situation. Somebody backed their trailer into the hood of my t680 last week while trying to park at a truck stop. I woke up during it so got them stopped, got their insurance, and took pics. Contacted their insurance about it, as well as mine, and just waiting for them to call back now.

It's just cosmetic damage. The hood still opens and the truck still drives. Hood just almost has a hole over the drivers side steer due to the trailer hitting it.

But I'm wondering what the best next option is:
Do I get it repaired myself now than send the invoice to the guys insurance later when they ask for it? Or would it be better to wait for them to get back with me after they talk to the driver and his company?

To throw a wrench into this, the hood also had existing damage due to a deer 2 years ago and the guy hitting the hood did make that a bit worse. That old damage might have already made the hood unrepairable.

 

It was also somewhat recorded by the cam on my drivers side mirror and sent to the insurance companies so will be hard for them to deny it.

While the cam doesn't show the actual contact (below the field of view), you can see the truck drive by before backing in with the company logo visible, back in getting right in front of the camera on the mirror putting the trailer license plate in view, see my truck shake from the hit, and see my hood lift and fall back down as he pulls forward after I got his attention. At the very least, it shows me stationary and him backing.

 

Stirred from sleep to loud crunching and the truck shaking. Than felt more shaking and heard more loud crunching, got up, saw what was happening, and pulled my airhorn to get him to stop backing. He pulled forward and got out to see what was going on.