You need to simply open the Lightroom Catalog from the backup location and then reconnect the images from the newer location.
Please check the following link for how to link the images in Lightroom : Adobe Lightroom - Find moved or missing files and folders
If the images are truly in the exact same file structure they were in previously, just right-click on the topmost folder and choose the option to update the folder location. Point Lightroom to where the images are now located. That should take care of it.
That worked but my structure is as follows:
In Lightroom only the individual folders show up. I have close to 100. Is there a way to change the display so I only have to relink the folder Lightroom Photos instead of each individual folder?
You should be able to just click on Lightroom Photos. All of the other folders are inside of it. Once you show Lightroom where that folder is, all of the others should synchronize as well. If Lightroom Photos isn't showing, right-click on one of the folders and choose to show the parent folder.