How to move LR photos from one Pictures folder to a different Pictures folder

Follow the step-by-step instructions (with screen captures) in this document under "Part 2 — Updating Folder Locations".

Adobe Lightroom - Find moved or missing files and folders

So, I am agreeing with JimHess​, don't move the photos inside of Lightroom; use the operating system to copy the files to the desired location and then point Lightroom to the new location.

You move them in Lightroom, from the folder they are in to the folder you want them to be in. The collections are just place holders, leave those alone in this process.

I suppose import presets could help. However, you are in complete control of where Lightroom imports your images. In the right-hand panel you can choose any hard drive and folder you wish.

Moving images from within Lightroom can be done using the drag/drop method. It is possible to drag a folder from one drive to another. A word of caution when doing that, however. Some have found that it's easy to drop the folder in a wrong or unknown location, and subsequently lose track of where the images are located. Then it becomes a challenge to get things linked all together again.

Personally, I prefer copying folders to new locations including new hard drives (Using Finder or File Explorer, not in Lightroom), and then using the library option to update the folder location, Directing Lightroom to the images in their new location. It's a good idea to keep the images in the same folder structure they were in previously. Then, after I have verified that Lightroom is finding Everything in the new location, I will use my operating system tools to remove the images in the old location. This will have no impact on your collections or any of your editing.