Why shielded? A twisted pair cable would be adequate in most cases.
Mine are made from 2 pair Cat5e and RJ12s.
The last Belkin shielded cable with RJ11/12 was about £10 for 1.5 metres
Given he may have a noise problem, for some reason he's losing bit-loading, might as well change everything as much as possible to narrow down the problem. What's a few quid when you've already replaced the VDSL modem?
I don't think it needs an earth. I think that's a drain wire in cases where you're screening HV cables and dangerous surface voltages build up on the screening - in aircraft for example.