Samsung will probably never be pushing Android 5.1.1 for the Galaxy S3 Neo but XDA has got us covered where several developers have provided custom S3 neo ROMs allowing users to taste the Android 5.1.1 lollipop on their devices. This Galaxy S3 Neo Motion ROM is the best one out there. Only three things are not working on it – NFC and FM radio. Other than that, this ROM is flawless. This is how Galaxy S3 Neo Motion ROM looks like. 
* Download ROM from below given link.
* Put it on SD card and flash using custom recovery
* After flashing – hard reset in custom recovery
After flashing ROM go to /system and edit last build.prop line from ro.multisim.simslotcount=1 to ro.multisim.simslotcount=2