Move the photos to wherever you want them to be, using your operating system. Keep the folder hierarchy intact, don't go moving photos or folders from one place in the hierarchy to another.
Then in Lightroom, reconnect via Adobe Lightroom - Find moved or missing files and folders
It also helps to reorganize things under a few top-level folders if they aren’t already, before moving them, so there are less reconnections to make after the move.
There have been some problems in the past for some people who use NAS or network drives for photos where a move loses files, so if that is what your external location is, then I’d suggest that you COPY the files and then rename the source folder(s) and then reconnect the photos in their new location and make sure everything is ok before deleting the photos off the original location on the internal drive.