I'd say bug. I ran into a bug end game today trying to attune to Garuda HM Atheryte which is supposed to give me acces to Garuda HM in Duty Finder and when I attune to it it says "Garuda HM unlocked in DF" but the quest never finishes and I can attune to it over and over repeatedly and nothing happens. I get the same message but no progress. I'm guessing there's some server issues which is why they have them down now for maintenance so maybe your friend can try again after they're up.
Cant help the first person since that mission worked perfectly for me, but i can help you.
You need to have a look at your seals. the HM Garuda unlock gives seals upon completion. If you're currently capped on seals (anyone would be by then, really) you cant actually finish the quest. Buy something from your GC, try again.
[XI] Surivere of Valefor
[XIV] Sir Surian Bedivere of Behemoth