Per this answer, the drivers for this device are now available, but require building libfprint
from source, using this fork. I was able to get this to work for my HP Envy with the same fingerprint reader and Ubuntu 22.04 by using
sudo apt-get install meson ninja-build libgusb-dev libgirepository1.0-dev libnss3-dev libgudev-1.0-dev gtk-doc-tools valgrind
sudo ldconfig
git clone https://gitlab.freedesktop.org/geodic/libfprint.git
cd libfprint/
git checkout elanmoc2
git pull
meson build
cd build
ninja
sudo ninja install
You may need to reset your fingerprint reader in the BIOS — I could not verify my right index finger until I reset the reader, but all my other fingerprints worked. To reset the reader, enter the BIOS, look under Security, and enable “Fingerprint Reset on Reboot”. Select “Yes” when asked to verify that you want to reset the reader — you will lose all current fingerprint data — and allow the computer to reboot. The BIOS setting will reset to “No”, so you do not need to re-enter the BIOS.
Now you can login and add fingerprints using Settings/Users or fprintd-enroll -f <finger>
.