https://ffxiclopedia.fandom.com/wiki/Star_Struck

Can't open this quest, despite having both items and Windurst reputation 7. (Rep 1 is required)

Oct 24, 2020 - same thing here. I have the Torn Epistle and the Meteorite in my inventory.

To me he's just saying (paraphrased): "I'm glad you found the stone! blahblahblah". Sounds like he's giving me the text from quest completion, but I'm not getting a reward and the item isn't being removed from my inventory.

I know I completed this quest, I just cant recall offhand what I did to do it because I had the same issue. Here's a few ideas to try :

1) Try talking to the npc's around him then him again.
2) Try moving the torn epistle to one of the mog bags then talk to him, then move back to inventory and try again.
3) Try dropping the torn epistle, talk to him, then go get another epistle and come back.

I know I tried a few different things then randomly it started working, best of luck.