The short version:
Welcome to Benq-Siemens mobile phone support. Where do I click on this program in front of me to get the answer you need?
And when I'd tell them where exactly they should click, they weren't trusting me.
It must be because I wasn't using the precise words they have on screen: the interface and user manual of my phone are in Italian, and I had to translate back to English. So I later downloaded the English manual. I was saying "phone lock code" when the English manual said "phonecode". I'm impressed.
So at some point I asked them: "Suppose that my phone is broken. Do you have a list of repair services near Manchester?".
Turns out they don't. The Benq-Siemens support center has no list of their own repair centers, and tells you (I swear) to google for it.
I'll wait to be back to Italy: I know where to go, there.
Conclusion: is there a SIP-VoIP software with a "record phone call" functionality? I don't know of any so far. Some things, if you just tell them, they're hard to believe.