login screen is not initially on the monitor that contains the mouse cursor

I have a dual-monitor setup (an external LED display connected to my laptop), and I use exclusively the external display while working at home (the laptop monitor is turned off).

  laptop monitor: 13.1", 1280×800
  external monitor: 23", 1920×1080

When I boot my laptop with the external display connected and switched on, lightdm recognizes both monitors and displays the login screen on the primary monitor (the laptop’s) and the ubuntu logo centered on the secondary display (the external one).

However the mouse cursor is initially positioned on the external monitor (I think it is horizontally centered on the virtual screen made up of the two monitors, i.e. (1280+1920) ÷ 2 = 1600), so I would expect the login screen to be displayed on the same monitor as the mouse cursor. Note that as soon as I move the mouse cursor from its original position, the login screen follows it, so the problem is visible only initially, and it fixes itself whenever I interact with the mouse.

I would expect either of the following two things to happen to fix this glitch:
 - have the mouse cursor initially centered on the primary monitor, where the login screen is
 - have the login screen initially positioned on the monitor that contains the mouse cursor

ProblemType: Bug
DistroRelease: Ubuntu 12.10
Package: lightdm 1.3.3-0ubuntu4
ProcVersionSignature: Ubuntu 3.5.0-15.23-generic 3.5.4
Uname: Linux 3.5.0-15-generic i686
NonfreeKernelModules: nvidia wl
ApportVersion: 2.5.2-0ubuntu4
Architecture: i386
CheckboxSubmission: 2c7995ffdf051a6d0adf7ab2c7be5ba9
CheckboxSystem: 7e42599bda39ea7ff8b528272b6ef52b
Date: Wed Sep 26 07:47:46 2012
EcryptfsInUse: Yes
InstallationMedia: Ubuntu 12.04 LTS "Precise Pangolin" - Beta i386 (20120328)
SourcePackage: lightdm
UpgradeStatus: Upgraded to quantal on 2012-08-30 (26 days ago)