I hate to cut and paste, but honestly I feel GOT wiki gives a good (and possibly the only) answer. Here it is.
Samwell, feeling guilty, tells Daenerys and Jorah Mormont that he "borrowed" Heartsbane. Samwell later gives his family's ancestral sword to Jorah (due to its Valyrian properties allowing it to kill White Walkers), who promises to wield it for the Battle of Winterfell to honor of his late father, Jeor Mormont, who Sam also saw as father figure. Towards the end of the Great Battle, Jorah fends off many wights in order to protect Daenerys, getting stabbed multiple times in the process and eventually succumbing to his wounds. The current owner of the Valyrian blade is unknown.
So honestly anyone or no one could have it.