WMP has a license management tool which allows licenses to be backed up and restored.
This isn't my area, but reading the associated help file in WMP (I've pasted it below), it would seem like you would need to backup the licenses and then restore them after the music files have been moved.
The access the tool, select TOOLS>License Management.
This is the section in the help file:
Understanding licensed files
Licensed or protected files are digital media files that are secured with a license to prevent illegal distribution. The license can specify whether it expires and how you can use the file. For example, a license can specify whether you can copy the file to a portable device. The terms of the license are specified by the person or company that provided the file. Windows Media Player cannot play protected files without a license.
There are different ways you can acquire licensed files, but the most common way is to download them from content providers (such as record companies). The content provider may issue a license when you download the file. Otherwise, when you play a file for which you do not have a license, Windows Media Player attempts to acquire one. You may be required to register or pay a fee first, depending on the content provider. If the Acquire licenses automatically for protected content check box is selected on the Privacy tab and the content provider does not require a fee or registration, the Player acquires the license without notifying you.
Another way to acquire licensed files is by copying CDs with the Copy protect music check box selected. By using this option, all the tracks you copy are protected files, and licenses are issued at the same time. The licenses for copied CD tracks allow you to play the tracks on your computer, transfer the tracks to a non-SDMI-compliant device, and copy (burn) the tracks to a CD.
You can manage your licenses by backing them up. By default, you are prompted to back up your licenses approximately two weeks after you acquire a new license. Because you can copy your licenses to a location other than your hard disk, you may be able to restore any lost licenses from the other location. For example, if you move licensed files to a new computer, you can use License Management in the Player on that computer to restore the licenses for the files. Microsoft tracks the number of times you attempt to restore licenses. The number of times you can restore your licenses on what is considered to be a "unique computer" is limited. For example, if you reformat your hard disk and reinstall Windows on a computer and your music files are on a different partition or computer, the reformatted computer is considered to be a unique computer when you restore the licenses.
Note that you should back up your licenses to a floppy disk periodically. If you reinstall or upgrade the operating system, your licenses may be lost even though you retained your protected files. For more information about backing up licenses, see To back up your licenses.
The following rules apply to licensed files:
You can play protected files until the license expires. You are informed of the terms, if any, when you acquire the license. Contact the content provider if you have questions about the license terms.
You cannot copy and share licenses among different computers. If you copy a licensed file to another computer or give a copy of the file to another person, you or the other person will need to acquire a new license for that computer. This process starts automatically when you play the file on the new computer.
You can use the Copy to CD or Device feature to copy licensed files to portable devices only if the license allows it.
