trying to switch authorized computer

[iMore Question]

So I figured once I synced my phone for the last time on my slow and dying laptop and backed it up on the old laptop, I would connect to the new computer and authorize the new computer. Then basically make my iphone push itself into the new computer or that the act of authorizing the new computer would mean it would automatically get all the info on the old computer.

The phone is still good. The songs on the phone moved to the new computer but the playlist structure is not there.

What am I missing?
thanks

 

[SwitchBeach]

Did you copy your iTunes library from the hard drive on the old computer to the hard drive on the new computer?