Yes you can, I do it myself lol. JUST MAKE SURE when you data transfer, the internet settings are on cable, if it isn't it will try to transfer thru wireless, and that won't work
all you do is on the 3.55 system wich is fat put the internet cable in both systems also known as eithernet cable on 3.55 you select option 1 ull get the cord picture leave it that on the slim ps3 ofw 4.00 same thing but option 2 but option 2 is the last step on the 3.55 hit x on the cable picture screen then on the slim hit option 2 then wait a few seconds ull get a message saying ur system will be formatted all ur data on ur slim will be lost everything on ur 3.55 will be on ur slim the more data you have the longer it will take hit yes then yes again then it will transfer good luck