If you want to do this manually, I wrote an "Object Copy/Paste" tool many years ago which allow you to select an object, copy it, select a target (which in your case would be a row in a browser) and paste it. The attribute data was untouched but the object was replaced (or added). There was a level of danger with this tool as there was no "are you sure?" check prior to the object paste, nor an undo. So, with this destructive power, some care was needed.
If this tool would be useful to you or anyone else, let me know and I'll dig it up. It was from the 32bit era and added "Object copy" and "Object paste" menu items to the Objects menu. The utility is very simple and I'm also happy to share the MapBasic source.