It could be that Ben’s parents were going to give it to him when he completed the Jedi training, perhaps not as a weapon but as a symbolic birthright. I imagine Han spending months tracking it down, asking Leia for help to try and find it, since they know how much Ben likes ‘that old historical stuff’.
Then after the breakup, and Leia not wanting it anywhere near her…
There could have been some really emotional stuff there.