If you get an error when moving Photos Library
Select your external storage device in the Finder, then choose File > Get Info.
If the information under Sharing & Permissions isn’t visible, click the triangle to see more.
External Drive Info window with “Ignore ownership on this volume” selected
Make sure that the “Ignore ownership on this volume” checkbox is selected. To change it, you might first have to click the lock button to unlock the setting. If the storage device isn’t formatted correctly for Mac, or was used for Time Machine backups but hasn’t been erased, this checkbox won’t be present or won’t be selectable after unlocking. In that case, erase the storage device first.
If you have some other permissions issue with your library, you might be able to resolve the issue with the Photos Library repair tool.