Here is the response from Kentico support
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I am afraid the URL selector form control was not designed to remember the tab and page which was selected last. If you need to keep this data, you would need to customize its code in the '/CMS/CMSModules/Content/FormControls/Documents/SelectPath.ascx'.
Regarding the link to the selected page, the system shows a virtual context link but when you save the changes, it is converted to a full link and saved to the database in a correct format.
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