Is better sati cause to better memory? Did Lord Buddha tell something about this ? (Relationship between sati and memory) 

There was a monk in Buddha's time who is enlightened but didn't have a strong memory. To be enlightened, some has to have a strong sati.
Normal memory is bound up in craving (e.g., "I remember that pretty face"). Or normal memory is bound up in aversion (e.g., "You ALWAYS pick on me!"). Or normal memory is bound up in delusion (e.g., "I want to be like that famous person").

The memory of sati requires awareness without craving, aversion or delusion. That's surprisingly difficult and requires steady and constant practice.


  AN5.14:4.1: And what is the power of mindfulness?  It’s when a noble disciple is mindful. They have utmost mindfulness and alertness, and can remember and recall what was said and done long ago.