The issue appears to be solved.
I noticed that HP had released a BIOS update (labeled as a May 11th release), and this BIOS update solved the issue. Indeed, one of the fixes listed for this update was “- Fixes an issue where the original boot entry is deleted when a third-party encryption software creates a boot entry.”
Secure Boot needed to be disabled, but then the Feature Update from 1809 to 1903 worked on the Probook G4 without killing the Checkpoint boot entry. We also updated the BIOS on several Elitebooks (G5) and the Windows update (from 1803 to 1903) worked.
What I do not understand is that when I contacted HP about this issue, they said to contact Windows, even as they were busy fixing it.