cannot change keyboard language when entering password after screen-saver lock

When the screen locks from inactivity and the keyboard text entry is not English, I cannot change it back to English, so I cannot enter my password (which is in latin characters). The language widget is non-operable. The "switch to next source" key combination doesn't work either.

Workaround: If I press enough keys ("Ctl-Alt-Del", I think), the screen flashes (redraws) and then I can use the language widget to change the language to English.

detailed description:
I installed Ubuntu 16.04 desktop recently and left the default settings for the screen saver (turn off after 5 minutes of inactivity and lock the screen). I have added Greek keyboard.
Because of the short screen saver time, I find the screen frequently locks. If the keyboard is set to Greek, before the screen locked (e.g. because I was writing a letter in Greek), then it is still Gr in the lock screen. The language widget menu is not responding.

The language widget works properly if I lock the screen from the power/login menu (top right corner).
My text entry settings has "Use the same source for all windows" checked.

ProblemType: Bug
DistroRelease: Ubuntu 16.04
Package: unity 7.4.0+16.04.20160715-0ubuntu1
ProcVersionSignature: Ubuntu 4.4.0-31.50-generic 4.4.13
Uname: Linux 4.4.0-31-generic x86_64
NonfreeKernelModules: zfs zunicode zcommon znvpair zavl
.tmp.unity_support_test.0:

ApportVersion: 2.20.1-0ubuntu2.1
Architecture: amd64
CompizPlugins: No value set for `/apps/compiz-1/general/screen0/options/active_plugins'
CompositorRunning: compiz
CompositorUnredirectDriverBlacklist: '(nouveau|Intel).*Mesa 8.0'
CompositorUnredirectFSW: true
CurrentDesktop: Unity
Date: Wed Aug 3 08:50:35 2016
DistUpgraded: Fresh install
DistroCodename: xenial
DistroVariant: ubuntu
GraphicsCard:
 Intel Corporation 2nd Generation Core Processor Family Integrated Graphics Controller [8086:0102] (rev 09) (prog-if 00 [VGA controller])
   Subsystem: Foxconn International, Inc. 2nd Generation Core Processor Family Integrated Graphics Controller [105b:0d78]
GsettingsChanges:
 b'org.compiz.core' b'active-plugins' b"['core', 'composite', 'opengl', 'compiztoolbox', 'copytex', 'commands', 'mousepoll', 'imgpng', 'vpswitch', 'wall', 'regex', 'grid', 'move', 'resize', 'place', 'snap', 'unitymtgrabhandles', 'session', 'animation', 'expo', 'fade', 'workarounds', 'scale', 'ezoom', 'unityshell']"
 b'com.canonical.Unity' b'minimize-count' b'100'
 b'org.gnome.desktop.interface' b'gtk-im-module' b"'gtk-im-context-simple'"
 b'org.gnome.desktop.interface' b'scaling-factor' b'uint32 1'
InstallationDate: Installed on 2016-07-28 (6 days ago)
InstallationMedia: Ubuntu 16.04 LTS "Xenial Xerus" - Release amd64 (20160420.1)
MachineType: To be filled by O.E.M. PLAISIOCOMPUTERS
ProcKernelCmdLine: BOOT_IMAGE=/boot/vmlinuz-4.4.0-31-generic root=UUID=5f8e6079-856e-4c75-9d89-3f92e62336be ro quiet splash vt.handoff=7
SourcePackage: unity
UpgradeStatus: No upgrade log present (probably fresh install)
dmi.bios.date: 02/28/2011
dmi.bios.vendor: American Megatrends Inc.
dmi.bios.version: AC3PGS02
dmi.board.name: H61MXV/H67MXV
dmi.board.vendor: Foxconn
dmi.modalias: dmi:bvnAmericanMegatrendsInc.:bvrAC3PGS02:bd02/28/2011:svnTobefilledbyO.E.M.:pnPLAISIOCOMPUTERS:pvrTobefilledbyO.E.M.:rvnFoxconn:rnH61MXV/H67MXV:rvr:
dmi.product.name: PLAISIOCOMPUTERS
dmi.product.version: To be filled by O.E.M.
dmi.sys.vendor: To be filled by O.E.M.
upstart.unity-panel-service-lockscreen.log:
 (unity-panel-service:6784): GLib-CRITICAL **: Source ID 4294967295 was not found when attempting to remove it

 (unity-panel-service:8171): GLib-CRITICAL **: Source ID 4294967295 was not found when attempting to remove it

 (unity-panel-service:8171): GLib-CRITICAL **: Source ID 4294967295 was not found when attempting to remove it
version.compiz: compiz 1:0.9.12.2+16.04.20160714-0ubuntu1
version.ia32-libs: ia32-libs N/A
version.libdrm2: libdrm2 2.4.67-1ubuntu0.16.04.1
version.libgl1-mesa-dri: libgl1-mesa-dri 11.2.0-1ubuntu2
version.libgl1-mesa-dri-experimental: libgl1-mesa-dri-experimental N/A
version.libgl1-mesa-glx: libgl1-mesa-glx 11.2.0-1ubuntu2
version.xserver-xorg-core: xserver-xorg-core 2:1.18.3-1ubuntu2.2
version.xserver-xorg-input-evdev: xserver-xorg-input-evdev 1:2.10.1-1ubuntu2
version.xserver-xorg-video-ati: xserver-xorg-video-ati 1:7.7.0-1
version.xserver-xorg-video-intel: xserver-xorg-video-intel 2:2.99.917+git20160325-1ubuntu1
version.xserver-xorg-video-nouveau: xserver-xorg-video-nouveau 1:1.0.12-1build2
xserver.bootTime: Wed Aug 3 07:16:04 2016
xserver.configfile: default
xserver.logfile: /var/log/Xorg.0.log
xserver.outputs:

xserver.version: 2:1.18.3-1ubuntu2.2