Archiving your pictures is a great way to preserve the memories that you have captured with your device's camera. I'm confident that we can partner together and get your pics transferred to your computer successfully. Let's start with what operating system do you have on your HP laptop? When you plugged your Galaxy S III to the computer using the USB cable, do you get the audio notification that the device has been connected? If not then a great place to start troubleshooting would be the device manager to check the drivers. Once you have done so, please reply with your findings.
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I'm glad you're getting that message! This is definitely a good sign that your device will be able to transver content to your computer. Which operating system do you have on your computer? Are you able to locate your device on your computer like you would a flash or jump drive when it's connected? Are you getting any error messages?
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