Grub install fails during Dual Boot Ubuntu 18.04 LTS Install with Win10Pro

[Tres Equis]

Original: Fujitsu LIFEBOOK E782 with Windows 10 Pro; one SDD, no further HDD

First installation of Ubuntu 18.04 LTS one week ago alongside Win 10 worked fine.
Booting the Desktop-CD from USB (with no needed UEFI setting changes) worked fine, partitioning with gparted and installation on Desktop-CD finished normally.
During booting always GRUB screen to choose between Ubuntu and Windows. --> Perfect.

BUT After first use of Windows 10: No GRUB menu anymore, but always direct start into Windows.
Reason!?: Fast boot was not deactivated. Deactivation did not solve the problem. (And in UEFI menu no secure boot options available that could be deactivated. And if these would be the reason, Ubuntu should not have worked before!?)

When entering boot options on startup and choosing Ubuntu (which is still at first boot position) nothing happens. Obviously second boot option "Windows" is always entered because first boot option "Ubuntu" fails.

BUT why is a priorly fully-working Ubuntu not usable anymore after one Windows start with first activated but meanwhile deactivated fast boot option?

My try: New install of Ubuntu in the same way like initially done - with the Ubuntu-Desktop from USB.
BUT NOW: During installation GRUB cannot be installed anymore - tried two times now.
During installation I left the boot loader installation location to default /dev/sda, although precisely the Windows bootloader is at /dev/sda2 because I read multiply times that in EFI mode this is detected automatically.
Detailed system info will hopefully be in the automatic debug information with the report.

Thanks for any help,
best regards!

ProblemType: Bug
DistroRelease: Ubuntu 18.04
Package: ubiquity 18.04.14.6 [modified: lib/partman/automatically_partition/question]
ProcVersionSignature: Ubuntu 4.15.0-29.31-generic 4.15.18
Uname: Linux 4.15.0-29-generic x86_64
ApportVersion: 2.20.9-0ubuntu7.2
Architecture: amd64
CasperVersion: 1.394
Date: Sat Dec 29 20:10:41 2018
InstallCmdLine: BOOT_IMAGE=/casper/vmlinuz file=/cdrom/preseed/ubuntu.seed boot=casper quiet splash ---
LiveMediaBuild: Ubuntu 18.04.1 LTS "Bionic Beaver" - Release amd64 (20180725)
SourcePackage: grub-installer
UpgradeStatus: No upgrade log present (probably fresh install)

[Launchpad Janitor (janitor)]

Status changed to 'Confirmed' because the bug affects multiple users.