Nope, you cannot even transfer from 4.11 to 3.55, sony doesnt allow you to do that, for example if you transfer 3.55 to 4.11, you will only have the data on your ps3 excluding the software.
You will need to have the cfw spoof-er which puts you 3.55 on 9.99 and will allow you to transfer any direction.
Originally posted by Gambler
No the firmware won't be changed, and yes you'll get your DLC stuff. :y:
Are you sure you can transfer to a lower firmware? i heard many responses that not possible unless a spoofer is used