Yes...you can use any of those 3rd party software....like Macrium, Acronis to do that. Also, depending on the SSD you buy.....some have migrating software that you can download that will do exactly that. Samsung's "Magician" Software is the only one I know of, off the top of my head. Check the SSD you're intending on buying website to see if they have a cloning software.
Or they could just install windows from an dvd/usb created by the Windows 10 media creation tool and start lovely and clean on the new SSD.
. As far as I am concerned, you have to restore the backup image that created by AOMEI Backupper only use the same software. It is true that you cannot restore it using other image software. AOMEI Backupper released new version 3.5 version. Maybe you can try that again.the AOEMI program would not produce viable W10 backup images to external media that would be restoreable.