Second instance of Garmin Express is not aware of the device firmware version that is stored in Garmin Connect

I have two instances of Garmin Express, on my laptop, a second on my desktop PC.

After updating an syncing my Edge 1040 the new firmware version is stored in Garmin Connect.
So far so good.

But when i then start my desktop without connecting the Edge to the computer, the Garmin Express instance there thinks that there is a firmware update available.

Obviously Garmin Express does look online in Garmin Connect about the actual software version.
I think it stores the device firmware version locally every time the device is connected via USB and therefor doesn't notice firmware updates that happened on another computer or by the device itself.

If Garmin Express is granted access to Garmin Connect this should be the place to store and get information about firmware versions.
If no access is granted than the current behaviour is o.k.