OK, so now
sudo lspci -v -s 02:00.0
but it looks like “Intel Wireless 3160” is the answer.
So you would need to grab that driver from a repository other than PureOS and then install it under PureOS. However you would first need to install PureOS on the gf laptop - without the internet (unless it has working ethernet). Your own laptop can be used to help with that.