Setting up a web of lies is a great way to guarantee that you'll be found out sooner or later. As a GM, you need to be on the lookout for any slip, because the characters are certainly going to notice these things that don't fit with what they previously knew. Picking up on inconsistencies is really just part of providing a realistic roleplaying experience.

Transcript

Boba Fett: Then my life will finally be able to begin. Free of the burden of the past. It is so close, I can taste it.
Han: Oh for goodness' sake...
Han: Obi-Wan is dead.
Han: Darth Vader killed him before the Peace Moon blew up. I was there. I was in it!
Han: She kept it from you to use you as a tool. This whole quest of yours is a waste of time. So please just stop monologuing about it!
{beat, stunned looks all round}
Lando: Wow. Good memory, Mr Amnesiac.
Han: ... or so Chewbacca told me anyway?