Though he may have declined to let it back his pictures up. Worth a try though in case it's there and he's just not thought about it.
Otherwise screen replacement may be the best chance. But not through an official service center as they'll almost certainly do a factory reset in the process of servicing the phone - you need to be clear to whoever does it that you want the data on it preserved.
If they'd set the default USB connection type to file transfer rather than charge only (via developer options) there would be a chance. But if the phone has been restarted since the accident you'll need a PIN to unlock it, at which point it wouldn't matter whether you'd set that or had USB debugging on even, you'd be stuck anyway.
I don't know whether it's possible to mirror the screen using a cable (hdmi interface) without unlocking and setting up. If that we're possible and if you already had a Bluetooth mouse or keyboard paired it would be possible to transfer via WiFi by installing and setting up an app. But there are two "ifs" there, the second being a big one, so I mention this just in case we're very lucky. I think the answers you've already had are more likely to bear fruit.
