Have an issue where one user can see and use the Advanced license, but another user can not see it as an available license to use.
Based on the image you provided, the ArcGIS Administrator is currently set to use the Desktop Standard license. Go back to the ArcGIS Administrator the click on the Desktop folder. Make sure the radial button is selected for Advanced (ArcInfo) Concurrent Use. Then click Apply. Go to the Availability folder and confirm you have Desktop Advanced listed. If so, you can close ArcGIS Administrator and start ArcMap or ArcCatalog.
Let me know if this is not the issue. We will need more information about the license manager and ArcGIS Administrator on each machine.
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