Access iPhone through emulation

My friend's iPhone just faded out today. The screen is just white when she turns it on. The apple store told her she is going to lose everything... this is stupid because I'm 100% positive a hard drive failure has not occurred. Alarms are still going off. Reminders work. Notifications are being received. We know this because each has it's own respective sound that is getting sporadically emitted.

When I hook the iPhone up to her computer to backup it's contents, it wants us to enter the phone's password. We are not able to simply enter the password into the blank white screen. The phone doesn't registered this touch input. Moreover, we've tried holding down every combination of buttons imaginable to make the screen responsible again to no avail. So I'm inclined to say that the screen completely failed.

So here's my question. Is there a way from the computer that I can mimic touch input on the iPhone to input the password to initiate the backup process? Is there another way to access the phone's file system recover it’s contents? The phone has been rooted, so it needs to be a legit strategy. The last iCloud backup was too long ago, in case anyone asks.

Thank you for any help, Nick

You can use VoiceOver to control the device from a USB keyboard. You can usually use a keyboard to enter the passcode, but you also need to press Trust from a keyboard, which you can't do while connected to a computer that is not already trusted. In essence, either

• enter the passcode with a USB keyboard and connect the device to a trusted computer, or
• use VoiceOver to control the device from a USB keyboard to perform a backup to iCloud, steps for which are provided at https://deciphertools.com/blog/iphone-passcode-broken-screen/.