For whom was Bilbo’s mithril coat forged?

[Valandil]

Originally Posted by Alcuin

In Chapter 16, “A Thief in the Night”,
and in Chapter 13, “Not at Home”,
:
:
:
Surely it stands to reason that the mithril armor was forged for the son of Girion Lord of Dale, paid for with Girion’s emerald necklace, and delivery was interrupted by Smaug’s arrival. The magnificence of the artifact was such that Thorin, the Elvenking, and Aragorn assumed that it must have been for an Elven-prince – unless, of course, they knew it was, and for whom it was made, in which case Legolas is an awfully young Elf.

So then... by rights, Bilbo's mithril coat should belong to Bard? Perhaps that part of their family history had not been passed along - and even if it was, I doubt Bard ever knew that Bilbo had it, or that Thorin or Bilbo ever had a thought about determining rightful ownership (after all - Dragon's plunder is fair game to all, right...).