I have Arch Linux installed with deepin desktop environment and lightdm. Greeter is lightdm-deepin-greeter. I have installed fprintd, configured fingerprint, i can successfully login to sudo with fingerprint, but not login in greeter. I have set files in /etc/pam.d to contain auth sufficient pam_fprintd.so.
Do you have your home dir encrypted? If yes, then it is not possible to easy way login with fingerprint.
You need your encryption passphrase to decrypt our home folder and fprintd does not have it. So it can log you in, but with no files in your home. So it just fails.
Try to set
auth sufficient pam_fprintd.so in
/etc/pam.d/lightdm instead of
lightdm-greeter, it works for me. BUT that's still far away from unlock with finger from resume to suspended state. In case you may ask about it soon, I afford the useful answers that I gathered here: fprint timing out and Fingerprint reader doesn't work after sleep.
I personally don't figure out a workaround yet ╮(╯▽╰)╭.