Yes. He checked. Full voltage leaving fuse block. ....
On the pic, did he check and find 3 volts at one of the connectors
for the low-beam relay? (that's the way the schematic and his writing made it look). If so, the schematic shows at least two simple opportunities for voltage loss along the way: the
connection into the 12-volt main for the Hi-beam relay, and if that connection is good, then
the high beam relay itself may be bad, causing a drawdown in voltage. Here is an easy thing to try: pull out the high beam relay, ....or... disconnect the 12 volts going into that high beam relay (is it one of the two in the twin relay? if so, you have to do the latter). Then use the light switch to turn on the low beams. If the low beams work, then the high beam relay is faulty and replacing it should solve things.
I'm going to be a bit contrary to what others have said, and say that the possibility that the wire itself has "gone bad" is very low (not impossible, but very low on probability scale compared to other possible causes). If there is a connector along the way, that is another story, but I believe it inadvisable to go poking into the wire casing -- I've seen many more problems
caused by that than fixed (you've just opened the wire for oxidation, and you often compromise a strand or two in the process). However, it is always a great idea to look along the wire casing for chafing if that can ever happen: in car wire harnesses, it is common for a wire to fail where you almost always find that the casing and then the wire have been chafed open and the wire compromised.
Again, best of luck... this kind of thing does get "fun" when you finally resolve the issue.
-Mitch