That, plus many other things. Rebuilding trust takes a lot of work for the offender and none from the betrayed, because the betrayed cannot rebuild truth in someone else.Unless he has corrected all the lies in that absurd story he gave you, I would not trust him.
It is important to wait and watch for a lengthy period of time. I'd say at least a year.The trouble is that often the 'pretending I have changed' carries on till they move back in together. The after a few weeks or months the cracks start to show.