Jon doesn't need that sword because he already has one that kills white walkers. Also, Sam doesn't need his old man's sword does he? Didn't already kill the white walker with dragonglass? He only took his father's sword because his old man pissed him off, right? I think that Sam will give his sword to Mormount and both of them will end up brokering the deal between Jon and Khalesi. Sam has I think learned pretty much all that he needed to know in order to help Jon except for the lineage question and maybe he finds that out also or Bran will educate everyone on Jon's family history.
So, I think that Sam is going to leave his wife and kid at the Citadel and go on to help his friend Jon while Jorah will follow his newly de-scaled pecker to wind up in the arms of his Khalesi