@azh_97 and @ll other who are interested:
It does not work the first time.
Don't know why, but I can tell you how I got it working with Charles:
Do all in the well known Vita-Charles how-to.
Install Charles, disable Windows Firewall, setup Proxy on Vita
select "test internet connection" on the VITA
download the psp2-updatelist.xml (attached to this post)
right click on the psp2-updatelist.xml?xxxxxxxxxx file entry in
http://fxx01.psp2.update.playstation.net/...
choose "Map local" and choose the psp2-updatelist.xml on your HDD
right click again and choose "Edit"
(left) click on the new "Edit entry"
in the right window, select "Query String"
click "Add" and add the variable "val" with the value "03000000"
It does still not work? continue:
with every "connection test" a new psp2-updatelist.xml?xxxxxxxxxx entry will appear under
http://fxx01.psp2.update.playstation.net/...
There will be one (or even more) with "Map local"
NOT active
repeat the step where you map your local psp2-updatelist.xml file
(you do NOT have to repeat the "Edit" steps)
Whenever I try it, it takes a few tries and "Map local" steps, but will work then!