If the bottle of molasses has been sealed and never opened the unopened and fully sealed bottle of molasses can last as long as 10 years on the shelf or in the pantry and maybe even longer if you refrigerate it.
Once opened but sealed after every use the molasses can last for up to 5 years in the refrigerator.
It may not be as fresh after 1 year but it's still good to use for up to 5 years after opening the molasses.