I'm sorry to say, but no, it does not help.
As stated in the opening post, the installed adapter is an Advanced-N 6230.
The versions of the PROset Tools installed is 15.3.1 at the moment (on the download page also referred to as "latest", but I also tried everything from 15.1.0 (also the 15.2.0 you mentioned) - none works.
So the situation is:
*A supported Intel® Centrino® wireless adapter is installed. - TRUE
*Version 15.2.0 of Intel® PROSet/Wireless Software is installed - TRUE
Still, the LITE Version is installed!
To make it even more clear:
* A non-supported Intel® wireless adapter is installed - NOT TRUE (6230)
* A non-Intel wireless adapter is installed - NOT TRUE (6230)
* A supported Intel Centrino wireless adapter is installed but the wrong version of Intel PROSet/Wireless Software is installed - NOT TRUE (15.3.1.0 according to help->about from within the PROset/Wireless software)