Would this be more like to be used in the 'general' sense, or in the 'remembering something specific' sense? For example, a common English phrase is something like "As a photographer, it is important to remember that your customers need to feel comfortable with you." - We don't really mean REMEMBER as in "Oh whoops, I forgot my customers need to be comfortable", we more mean "Remind yourself of that because it tends to slip away otherwise". Then there is a detective questioning someone "It is important that you try to remember as much as you can...." sort of thing. That's actually an act of remembering rather than just a not-letting-become-unimportant thing. Is this Swedish more likely to be one or the other (perhaps this goes with the "kommer ihåg" question)?