This is addressed in the film's official novelisation. In short, they sold it and used the funds to upgrade the Serenity.
This [The Serenity] was Mal's pride and joy. A while back, they got their hands on
one of the few remaining Lassiters, one of the early laser pistols.
Expensive as hell, they'd lifted it from right under the nose of a
rich gent name of Durran from his estate on Belerophon. Took a spell
to find a buyer for so major an item, but a buyer they did find, and
the funds went to purchase a fancy new mule.
Inara seemed to think that she knew people who could afford it, so it's possible that one of her contacts ended up taking it off them for a fat fee.
MAL: It's like something out of a fable! I've got this priceless artifact, the biggest score of my unseemly career, and no one will
INARA: The Lassiter's universally known. Fencing it is like... fencing the Mona Lisa.
MAL: Well... Mona Who?
INARA: You're out of your league. You should consider my offer --
MAL: I done thinking about that, and you ought to stay clear.
INARA: I know people in the highest ranks of --
MAL: Jabber jabber jabber. I ain't listening. Just 'cause you helped out on the job don't make you a crook. I will not have you
jeopardizing your career over this.
As to the proceeds of the sale, by the time of the film Serenity (supposedly set several months later) we see that the ship has been radically overhauled with a much larger dining area, a dedicated ship's kitchen, a medical bay with a fancy new medi-bed and all sorts of scanners and gizmos, not to mention that the exterior seems to be sporting a new wing design and the flashy new hover-mule.
It seems reasonably likely that that sort of work would require a lot of money, the kind of cash you'd get from selling a priceless artifact, even at a whomping discount.