Both computers are able to access the internet.
The host's network places does not contain the previously mentioned shared folder.
Host can ping its own adapter, the default gateway and just recently the 2nd PCs adapter. Up to this all pings were timed out
2nd PC can't ping its own adapter, the default gateway or the host. All pings were timed out. Yet it's the only PC at the moment able to transfer files!
Windows firewalls on both PCs allow exceptions for file sharing.
I could do with a dig-out here.