Hi Spr,
Follow below steps
1) Upgrade OS from RHEL 5.3 to 6.0
2) Upgrade database from 11.2.0.2 to 11.2.0.4 including SBP similar to System A
3) Perform full backup of system A
4) Restore the backup to system B.
5) Perform post restore activities.
Regards,
Deepak Kori