Did you recently upgrade to 2016? The most common cause for HII crashing is if you are using a PXE rep from an older version. If you did not redeploy pxe reps after upgrading, redeploying them may solve the issue with HII crashing.
There is an alternative method to id the correct driver:
Keep in mind with LDMS 2016 and a UEFI bios, you'll be using 64 bit WinPE so you want to locate 64 bit Win 10 drivers for that dongle. If HP doesn't have them available try Intel (if your NIC is an intel nic). I'd download all that are available and try loading them manually in WinPE, reinitializing the network stack between each one, until you get a valid IP. That way you know specifically which driver needs to be injected to your boot.wim.
We did upgrade to 2016 and I have been able to load the NIC into the PE boot. We don't use PXE boot but I found the solution. I found that you need to install a LD agent on the workstation first so it fills out the model in the HII db. Otherwise the program will crash.