This has happened to me on many occasions. I think the prerequisite is to simply sell any Dwarven weapon or armor piece to any merchant. Then there will be a good chance you'll receive a letter,
However, after retrieving the requested Dwarven item and selling it to Calcelmo, the quest ends there. Nothing more happens...
I think the only trigger is you buying a Dwarven item, if you sell or loose the item any identical item is meant to work for the quest but i've never tested that (and i think he'll only ask for one at a time).