For some reason, Samsung did not include USB mass storage mode and users, thus are forced to use the MTP mode. We highlighted this Galaxy S3 bug earlier too and after some days, folks at XDA released an app called Easy UMS that allowed users to access the micro SD card slot. This worked like a charm on all International versions and AT&T version. For some reason, it did not work as expected on my T-Mobile Galaxy S3.
While its developer confirms that it is compatible (and yes it it), the Galaxy S3 USB mass storage app does not works right away. After you have rooted your T-Mobile Galaxy S3; installed CWM and the APK, start the SGS3 Easy UMS app and connect it to your computer. It will connect using the normal MTP mode. Now, tap on UMS mode.
Now follow these steps:
1. On your Windows 7 computer you will see it will try to install “SAMSUNG Mobile MTP Device” as one of the drivers and fail *this is normal*
2. Go into Device Manager on your computer, right click “SAMSUNG Mobile MTP Device” and select “Properties”
3. Click on the “Driver” tab and click the “Update Driver” button, a prompt will then come up
4. Select “Browse my computer for driver software”, then select “Let me pick from a list of device drivers on my computer” on the next screen
5. Select “USB Mass Storage Device” as the new driver from that list and finish up that install
6. At the end you will see something like this on your computer – Screenshot Here
7. Windows will install final drivers automatically and a new “Disk drive” will show up on your computer, this is your external SD card on your device
Keep in mind that it is not possible to get access to the internal storage as USB mass storage device.