The eReader is authorized/activated with an AdobeID rather than with a computer.
It is possible to have multiple computers and multiple devices all authorized with the same ID.
The eReader gets its authorization when you Authorize Device from any computer;
and then should work find when connected to any other computer authorized with the same ID.
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One possible reason for your issue is that you haven't authorized the laptop with your AdobeID.
In that case ADE generates an anonymous/implicit ID with very limited capabilities.
In particular, one capability missing is the ability to pass the implicit ID onto a device;
so it is possible (???) that in that case ADE does not show the device.
If that is the case
- ctrl-shift-D to ADE (cmd-shift-D if it's a Mac) on the laptop to remove the anonymous ID
- restart ADE (maybe not needed)
- authorize ADE with the same ID as you are using on the desktop
- restart ADE (maybe not needed)
- plug in the eReader and see if it is recognized