Key is to stitch the SHSH file with ipsw
Prior to downgrading, there are a few things you need to have :
1. Your device should be an A4 device or lower (Iphone 4 and older models)
2. Latest version of Redsnow 0.9.14.b2 (Download Mac or Windows)
3. Download 5.1.1 IPSW
4. Your saved SHSH Blobs.
Once you are done downloading everything, sit back and follow these steps :
1. Copy and Paste your SHSH Blobs into the same folder as your 5.1.1 IPSW.
2. Open Redsnow (Run as Administrator in Windows)
3. Put your device running iOS 6 into DFU mode
4. In Redsnow, go to Extras > SHSH Blobs > Stitch
5. Click IPSW and select the 5.1.1 IPSW
6. Click Local (for Blobs stored on PC)
7. Once both of them are selected, Redsnow will start stitching your firmware with your SHSH Blob. This is done because Apple has stopped signing iOS 5.1.1, but using this firmware you will be able to downgrade to 5.1.1.
8. In RedSn0w, go back two pages, and click Pwned DFU. This will place your device into Pwned DFU mode so that iTunes can restore using the stitched firmware. Without doing this, you will get error 1600 in iTunes.
9. Open iTunes and it will detect your phone in Recovery Mode. Click on Restore holding the option key (Shift key for Windows) and select the newly built IPSW (filename will be prefixed with 13 numbers which is your device's ECID)
10. iTunes may give you an error (-1), Do not panic.
11. Open Redsnow > Recovery Fix
12. Put your device back into DFU mode, and the recovery fix should run successfully.
13. Once it gets out of Recovery fix, yout device will be running on 5.1.1.
If you get stuck or get any other error message, feel free to comment below. It will help other to fix those.
