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Re: How do I move my pictures to external hard drive?
For moving ALL photos, it is recommended you do that using COPY in the Operating System (Lightroom shut-down).
And use the OS to compare the copy to insure all files have copied correctly.
Open Lightroom, then with the new drive connected- use the "Update Folder Location" to point the top-most photo folder to the new location. This will re-link all photos in their new location. Later the 'old' photo versions can be deleted from the internal drive. (and you do have other backups -naturally!)
"Space on the desktop."
Windows computers have a limit to the number of files that can exist on the desktop (including any folders) so it is a poor idea to use the Desktop for storage. Better to use a folder like "Documents", etc, or the external drive as you are intending.