Step 1: Creating a Temporary Home
The process of getting files from one memory card to another will require the use of a PC with enough free hard drive space to temporarily store the files. It's easier - and faster - if you have a memory card reader attached to your Windows PC, but in the interest of universality, we'll make the transfer using only your Windows Mobile Smartphone or Pocket PC and USB sync cable/cradle.
The first step is creating a temporary home for your existing memory card's files. Open My Computer (by clicking the icon on your Windows Desktop or by clicking Start > My Computer). Open your C Drive. With the C Drive open, click File > New > New Folder and give the folder a label you'll remember, like Card Storage:
Step 2: Getting Your Existing Files
Next, we need to locate and duplicate your SD (or other type of memory format) card's files. This will be done with ActiveSync (XP) or Windows Mobile Device Center (Vista). Insert the existing flash memory card into your Windows Mobile device memory card slot and connect the handheld to your Windows PC. Allow ActiveSync or WMDC to complete its syncing process. When syncing is complete, click the Explore button on the ActiveSync toolbar (or File Management > Explore the Contents of your Device in Windows Mobile Device Center). These tools allow you to browse the files stored on your Windows Mobile handheld from within Windows:

In the main "My Windows Mobile-Based Device" root folder (which usually reads as
), find the folder labeled Storage Card (seen above), SD Card, CF Card, etc (the actual name of the folder varies from device to device). This folder represents the full contents of your flash memory card. Open the folder and, using your mouse, select all of its contents by clicking Edit > Select All. When all of the files have been highlighted, click Edit again and select Copy.
You've now instructed your Windows PC to prepare to copy the entire contents of your flash memory card to your PC's hard drive. It is very important that you do not close the window, but minimize it to your toolbar.

Step 3: Copy the Files from the Old Card to Your PC's Hard Drive
You are now ready to copy the files to your PC for temporary storage. In My Computer, navigate to the folder you created. In our case, the folder name is Card Storage. When viewing the contents of the folder (which should still be empty), click Edit > Paste. The contents of your memory card will begin transferring to your hard drive. Make sure that the Explore window is still open on your PC.

Depending on the size of your old memory card, this process could take some time. Allow the transfer to complete. When it does, the folder you created on your C Drive will contain the exact contents of your existing memory card:

Step 4: Transfer Files to New Flash Memory Card from Your PC's Hard Drive
Okay, only one step to go: copying the files from your PC's hard drive to the new flash memory card. With the Pocket PC synced, remove the old memory card from your Pocket PC and insert the new card. In ActiveSync, again click the Explore button (or File Management > Explore the Contents of your Device in Windows Mobile Device Center) to view the files on your handheld within Windows. Navigate to the folder that represents your new flash memory card. The folder name will be the same that it was before, in our case Storage Card:

Because the new card is empty, this folder will now also be empty.
Leaving the Explore window open, in My Computer navigate to the folder on your C Drive containing the temporary files. When viewing its contents, select Edit > Select All from the toolbar, then Edit > Copy. Return to the Explore window with the memory card folder open and click Edit > Paste. The files stored on your hard drive will be copied to the new card. Allow the transfer process to finish.
The transfer is now complete. Your new flash memory card contains the exact files, in the same folder structure as before, but with more free space.
Final Thoughts
Feel free to delete the temporary folder you created on your C Drive once you've established that the transfer to your new card has been successful. You can also keep this folder as an archive backup on your hard drive.
If you wish to sell your old memory card, be sure to erase all of the files stored on it. This is most easily done with a Windows Mobile application that formats flash memory cards, such as Pocket Mechanic. If you happen to have a flash memory card reader attached to your PC, you can also format the card from within Windows.